Chapter 7/8: Geometry, Trigonometry, and Right Triangles



Chapter 7/8: Geometry, Trigonometry, and Right Triangles

|1. In right triangle ABC, hypotenuse AB = 10 and m[pic]B = 53. Find AC to the nearest integer. |

|  6 |

|  8 |

|  13 |

|  15 |

| |

|2. In rectangle ABCD, AD = 10, CD = 8, and diagonal [pic] is drawn. Find, to the nearest degree, m[pic]CAD. |

|  36° |

|  39° |

|  51° |

|  54° |

| |

| |

|3.   |

|[pic] |

|In the diagram of rectangle ABCD, AC = 22 and m[pic]CAB = 24. |

|(a)  To the nearest integer, AB = [pic]units. |

|(b)  To the nearest integer, BC = [pic]units. |

|(c)  Using the results from parts (a) and (b), the area of ABCD is [pic]square units. |

| |

| |

|4.  _________ |

|[pic] |

|In the diagram, the slope of the ascent of an aircraft is 7/50. Find m[pic]x, the angle of elevation, to the nearest degree. |

|  6° |

|  8° |

|  12° |

|  15° |

| |

|5. In right triangle ABC, if m[pic]C = 90 and sin A = 3/5, cos B is equal to |

|  3/5 |

|  4/5 |

|  3/4 |

|  4/3 |

| |

| |

|6.  _________ |

|[pic] |

|In right triangle BCD, BD = 12, m[pic]C = 90, and m[pic]DBC = 47.  Find DC to the nearest tenth. |

|  8.2 |

|  8.8 |

|  12.9 |

|  16.4 |

| |

|7. If tan A = [pic], what is the measure of [pic]A to the nearest degree? |

|  79° |

|  60° |

|  30° |

|  27° |

| |

|8. If [pic], what is the value of y to the nearest tenth? |

|  13.6 |

|  14.6 |

|  18.6 |

|  27.3 |

| |

|[pic] |

|9. In the diagram of right triangle ABC, [pic]C is a right angle.  Which equation is valid for [pic]ABC? |

|[pic] |

|[pic] |

|[pic] |

|[pic] |

| |

| |

|10.  _________ |

|[pic] |

|The tailgate of a truck is 2 feet above the ground. The incline of a ramp used for loading the truck is 11°.  Find, to the nearest tenth of a foot, the |

|length of the ramp. |

|  0.4 feet |

|  2.0 feet |

|  5.3 feet |

|  10.5 feet  |

| |

| |

|11.  _________ |

|[pic] |

|In the diagram of [pic]CDE, m[pic]D = 90, m[pic]C = 28, and ED = 15. Which equation can be used to find CD? |

|[pic] |

|[pic] |

|[pic] |

|[pic]  |

| |

|12. A 100-foot wire is extended from the ground to the top of a 60-foot pole, which is perpendicular to the level ground. To the nearest degree, what |

|is the measure of the angle that the wire makes with the ground? |

|  31 |

|  37 |

|  53 |

|  59 |

| |

| |

|13.   |

|[pic] |

|In the diagram of right triangle LPG:  [pic], LG = 52, LP = 20, and m[pic]NLP = 35. |

|(a)  To the nearest integer,  PN = [pic]. |

|(b)  To the nearest integer,  GN = [pic]. |

|(c)  To the nearest degree,  m[pic]GLN = [pic]. |

| |

|[pic] |

|14. In right triangle ABC, m[pic]C = 90, m[pic]A = 63, and AB = 10.  If BC is represented by a, then which equation can be used to find a? |

|[pic] |

|a = 10 cos 63° |

|[pic] |

|a = tan 27° |

| |

| |

|15.   |

|[pic] |

|In the diagram of [pic]ABD, altitude AD = 13, [pic] [pic] [pic], and m[pic]BAC = 70. |

|(a)  To the nearest tenth, BC = [pic]units. |

|(b)  To the nearest tenth , the area of [pic]ABC = [pic]square units. |

|(c)  To the nearest tenth , the perimeter of [pic]ABC = [pic]units. |

| |

|16. If tan A = 0.5400, find the measure of [pic]A to the nearest degree. |

|  28 |

|  29 |

|  33 |

|  57 |

| |

| |

| |

|[pic] |

|17. In the diagram of isosceles triangle KLC:  [pic] [pic] [pic], m[pic]K = 53, altitude [pic] is drawn to leg [pic], and LA = 3.  To the nearest |

|integer, the perimeter of [pic]KLC is [pic]units. |

| |

|18. In isosceles triangle ABC, AC = BC = 20, m[pic]A = 68, and [pic] is the altitude to side [pic]. What is CD to the nearest tenth? |

|  49.5 |

|  18.5 |

|  10.6 |

|  7.5 |

| |

| |

|19.   |

|[pic] |

|In the diagram of rectangle ABCD, diagonal [pic] is drawn, DE = 8, [pic], and m[pic]DAC = 55. To the nearest integer, the area of rectangle ABCD = |

|[pic]square units. |

| |

|20. If tan A = 1.3400, find the measure of [pic]A to the nearest degree. |

|  52 |

|  53 |

|  54 |

|  55 |

| |

|[pic] |

|21. In the diagram of right triangle ABC, b = 40 centimeters, m[pic]A = 60, and m[pic]C = 90. Find the number of centimeters in the length of side c. |

|40 |

|60[pic] |

|80 |

|80[pic] |

| |

| |

|22.  _________ |

|[pic] |

|In the diagram of right triangle ABC, [pic] is the hypotenuse, AC = 3, BC = 4, and AB = 5. Sin B is equal to |

|  sin A |

|  cos A |

|  tan A |

|  cos B |

| |

|23.If tan A = 0.4548, find the measure of [pic]A  to the nearest degree. |

|  22 |

|  23 |

|  24 |

|  25 |

| |

|24.The straight string of a kite makes an angle of elevation from the ground of 60°. The length of the string is 400 feet.  What is the best |

|approximation of the height of the kite? |

|  200 ft. |

|  250 ft. |

|  300 ft. |

|  350 ft. |

| |

|25.What is the perimeter of an equilaterial triangle whose height is 2[pic]? |

|6 |

|12 |

|6[pic] |

|12[pic] |

| |

| |

|26.  _________ |

|[pic] |

|A person standing on level ground is 2,000 feet away from the foot of a 420-foot tall building, as shown in the accompanying diagram.  To the nearest |

|degree, what is the value of x? |

|  12° |

|  21° |

|  76° |

|  78° |

| |

| |

|27.   |

|[pic] |

|The accompanying diagram represents a tree.  To the nearest tenth of a foot, the height of the tree is [pic]feet. |

| |

|28.A 10-foot ladder is to be placed against the side of a building. The base of the ladder must be placed at an angle of 72° with the level ground for a|

|secure footing. To the nearest inch, the base of the ladder should be placed [pic]inches from the side of the building and should reach [pic]inches up |

|the side of the building. |

| |

|[pic] |

|29.A surveyor needs to determine the distance across the pond shown in the accompanying diagram. She determines that the distance from her position to |

|point P on the south shore of the pond is 175 meters and the angle from her position to point X on the north shore is 32°. Rounded to the nearest meter,|

|the distance, PX, across the pond is [pic]meters. |

| |

| |

|30.   |

|[pic] |

|A wall is supported by a brace 10 feet long, as shown in the diagram.  If one end of the brace is placed 6 feet from the base of the wall, the brace |

|reaches [pic]feet up the wall. |

| |

|31.A ship on the ocean surface detects a sunken ship on the ocean floor at an angle of depression of 50°. The distance between the ship on the surface |

|and the sunken ship on the ocean floor is 200 meters. If the ocean floor is level in this area, how far above the ocean floor, to the nearest meter, is |

|the ship on the surface? |

|[pic]meters |

| |

|32.An airplane is climbing at an angle of 11° with the ground. Find, to the nearest foot, the ground distance the airplane has traveled when it has |

|attained an altitude of 400 feet. |

|[pic]feet |

| |

|33.In the accompanying diagram, x represents the length of a ladder that is leaning against a wall of a building, and y represents the distance from the|

|foot of the ladder to the base of the wall. The ladder makes a 60° angle with the ground and reaches a point on the wall 17 feet above the ground. Find |

|the number of feet in x and y. Round your answers to the nearest tenth of a foot. |

|[pic] |

|x = [pic]feet |

|y = [pic]feet |

| |

|34.As seen in the accompanying diagram, a person can travel from New York City to Buffalo by going north 170 miles to Albany and then west 280 miles to |

|Buffalo. |

|[pic] |

|a If an engineer wants to design a highway to connect New York City directly to Buffalo, at what angle, x, would she need to build the highway? Find the|

|angle to the nearest degree. |

|[pic]° |

|b To the nearest mile, how many miles would be saved by traveling directly from New York City to Buffalo rather than by traveling first to Albany and |

|then to Buffalo? |

|[pic]miles |

| |

|35.In the accompanying diagram of right triangle ABC, AB = 8, BC = 15, AC = 17, and m[pic]ABC = 90. |

|[pic] |

|What is tan[pic]C? |

|[pic] |

|[pic] |

|[pic] |

|[pic] |

| |

|36.In the accompanying diagram, the base of a 15-foot ladder rests on the ground 4 feet from a 6-foot fence. |

|[pic] |

|a If the ladder touches the top of the fence and the side of a building, what angle, to the nearest degree, does the ladder make with the ground? |

|[pic]° |

|b Using the angle found in part a, determine how far the top of the ladder reaches up the side of the building, to the nearest foot. |

|[pic]feet |

| |

| |

|37.The angle of elevation from a point 25 feet from the base of a tree on level ground to the top of the tree is 30°. Which equation can be used to find|

|the height of the tree? |

|tan 30° = [pic] |

|cos 30° = [pic] |

|sin 30° = [pic] |

|302 + 252 = x2 |

| |

|38.Which ratio represents cos A in the accompanying diagram of ABC? |

|[pic] |

|[pic] |

|[pic] |

|[pic] |

|[pic] |

| |

|39.Which quadrilateral must have diagonals that are congruent and perpendicular? |

|rhombus |

|square |

|trapezoid |

|parallelogram |

| |

|40.The accompanying diagram shows a flagpole that stands on level ground. Two cables, r and s, are attached to the pole at a point 16 feet above the |

|ground. The combined length of the two cables is 50 feet. If cable r is attached to the ground 12 feet from the base of the pole, what is the measure of|

|the angle, x, to the nearest degree, that cable s makes with the ground? |

|[pic] |

|Answer: [pic]° |

| |

|41.A tree casts a shadow that is 20 feet long. The angle of elevation from the end of the shadow to the top of the tree is 66°. Determine the height of |

|the tree, to the nearest foot. |

|Answer: [pic]feet |

| |

|42.As shown in the accompanying diagram, a ladder is leaning against a vertical wall, making an angle of 70° with the ground and reaching a height of |

|10.39 feet on the wall. |

|[pic] |

|a Find, to the nearest foot, the length of the ladder. |

|Answer: [pic]feet |

|b Find, to the nearest foot, the distance from the base of the ladder to the wall. |

|Answer: [pic]feet |

| |

|43.A person measures the angle of depression from the top of a wall to a point on the ground. The point is located on level ground 62 feet from the base|

|of the wall and the angle of depression is 52°. How high is the wall, to the nearest tenth of a foot? |

| |

| |

|44.From a point on level ground 25 feet from the base of a tower, the angle of elevation to the top of the tower is 78°, as shown in the accompanying |

|diagram. Find the height of the tower, to the nearest tenth of a foot. |

|[pic] |

|Answer: [pic] feet |

| |

| |

|PYTHAGOREAN THEOREM |

|1.If the hypotenuse of a right triangle is 6 and one leg is 5, the other leg is |

| [pic] |

|61 |

| [pic] |

|11 |

| |

|2.A rectangular lot that is 60 feet by 80 feet has a straight diagonal pathway. What is the length, in feet, of the diagonal |

|pathway? |

| [pic] |

|140 |

|20 |

|100 |

| |

|3.If the length of a rectangle is 3 and the width is 2, the length of the diagonal is: |

| [pic] |

| [pic] |

|5 |

|13 |

| |

|4.The length of the hypotenuse of a right triangle is 20 centimeters and the length of one leg is 12 centimeters. The length of |

|the other leg is: |

|  8 cm |

|  16 cm |

|  32 cm |

|  36 cm |

| |

|5.If the legs of a right triangle have measures of 9 and 12, what is the length of the hypotenuse? |

|  5 |

|  10 |

|  15 |

|  21 |

| |

|6.A wire reaches from the top of a 13-meter telephone pole to a point on the ground 9 meters from the base of the pole. What is |

|the length of the wire to the nearest tenth of a meter? |

|  15.6 |

|  15.8 |

|  16.0 |

|  16.2 |

| |

|7.The length of the hypotenuse of a right triangle is 15 and the length of one leg is 12. Find the length of the other leg. |

|  16 |

|  9 |

|  3 |

|  19 |

| |

|8.In a right triangle, the length of the hypotenuse is 12 and the length of one leg is 8. What is the length of the other leg? |

|[pic] |

|[pic] |

|[pic] |

|4 |

| |

|[pic] |

|9.A 10-foot ladder is placed against the side of a building, as shown in Figure 1. The bottom of the ladder is 8 feet from the |

|base of the building. In order to increase the reach of the ladder against the building, it is moved 4 feet closer to the base |

|of the building, as shown in Figure 2. To the nearest foot, how much further up the building does the ladder now reach? |

|  1 foot |

|  3 feet |

|  6 feet |

|  9 feet |

| |

|10.In right triangle ABC, AC = 40, CB = 9, and m[pic]C = 90. Find AB. |

|7 |

|[pic] |

|41 |

|49 |

| |

| |

|11.  _________ |

|[pic] |

|In which of the accompanying figures are segments [pic] and [pic]perpendicular? |

|figure 1, only |

|figure 2, only |

|both figure 1 and figure 2 |

|neither figure 1 nor figure 2 |

| |

|12.Katrina hikes 5 miles north, 7 miles east, and then 3 miles north again. To the nearest tenth of a mile, how far, in a |

|straight line, is Katrina from her starting point?  |

|[pic]miles |

| |

|13.The set of integers {3,4,5} is a Pythagorean triple. Another such set is |

|{6, 7, 8} |

|{6, 8, 12} |

|{6, 12, 13} |

|{8, 15, 17} |

| |

|14.How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will reach a point on |

|the house 36 feet from the ground? |

|[pic]feet |

| |

|15.If the lengths of the legs of a right triangle are 5 and 7, what is the length of the hypotenuse? |

|[pic] |

|2[pic] |

|2[pic] |

|[pic] |

|  |

| |

|16.The NuFone Communications Company must run a telephone line between two poles at opposite ends of a lake, as shown in the |

|accompanying diagram. The length and width of the lake are 75 feet and 30 feet, respectively. |

|[pic] |

|What is the distance between the two poles, to the nearest foot? |

|105 |

|81 |

|69 |

|45 |

| |

|17.In the accompanying diagram, a ladder leaning against a building makes an angle of 58° with level ground. If the distance |

|from the foot of the ladder to the building is 6 feet, find, to the nearest foot, how far up the building the ladder will reach.|

|[pic] |

|Answer: [pic]feet |

| |

|18.The accompanying diagram shows a kite that has been secured to a stake in the ground with a 20-foot string. The kite is |

|located 12 feet from the ground, directly over point X. What is the distance, in feet, between the stake and point X? |

|[pic] |

|Answer: [pic]feet |

| |

|19.A builder is building a rectangular deck with dimensions of 16 feet by 30 feet. To ensure that the sides form 90° angles, |

|what should each diagonal measure? |

|16 ft |

|30 ft |

|34 ft |

|46 ft |

| |

|20.Two hikers started at the same location. One traveled 2 miles east and then 1 mile north. The other traveled 1 mile west and |

|then 3 miles south. At the end of their hikes, how many miles apart are the two hikers? |

|Answer: [pic] miles |

| |

|21.In the accompanying diagram of right triangles ABD and DBC, AB = 5, AD = 4, and CD = 1. Find the length of [pic], to the |

|nearest tenth. |

|[pic] |

|Answer: [pic] |

| |

|AREA AND PERIMETER |

|1.What is the radius of a circle whose circumference is 16[pic]? |

|  32[pic] |

|  16 |

|  8[pic] |

|  8 |

| |

|2.The lengths of the sides of a triangle are represented by 3x [pic]4, x + 2, and 4x. Express the perimeter of the triangle as a|

|binomial in terms of x. |

|  8x [pic]2 |

|  8x + 2 |

|  7x [pic]6  |

|  6x [pic]4 |

| |

|3.Express, in terms of [pic], the area of a circle whose radius is 6. |

|  6 + [pic] |

|  6[pic] |

|  36[pic] |

|  360[pic] |

| |

|4.The area of a rectangle is represented by 32x3. If the length of this rectangle is 4x, then the width is |

|  16x2 |

|  16x3 |

|  8x2 |

|  8x3 |

| |

|5.In rectangle ABCD, AB is represented by 2x + 1 and BC is represented by x + 3. Express the area of rectangle ABCD as a |

|trinomial in terms of x: |

|  3x + 4 |

|  2x2 + 5x + 3 |

|  2x2 + 7x + 3 |

|  6x + 8 |

| |

|6.The area of a circle is 25π. What is the length of a radius of the circle? |

|  5 |

|  2 |

|  25/2 |

|  25 |

| |

|7.The perimeter of a square is 20x [pic]4. Which expression represents a side of the square in terms of x? |

|  5x |

|  10x [pic]2 |

|  8x [pic]16 |

|  5x [pic]1 |

| |

|8.If each side of a rectangle is doubled, the area of the rectangle will |

|  double |

|  be multiplied by 4 |

|  be divided by 2 |

|  remain the same |

| |

|9.What is the length of the radius of a circle whose area is 100[pic]? |

|  5 |

|  10 |

|  20 |

|  25 |

| |

|10.In a trapezoid, the smaller base is 3 more than the height, the larger base is 5 less than 3 times the height, and the area |

|of the trapezoid is 45 square centimeters. Use an algebraic solution to find the height, in centimeters, of the trapezoid. |

|The height of the trapezoid is [pic]centimeters. |

| |

|11.A circle has a radius of 5. Express, in terms of π, the circumference of the circle. |

|  π/5 |

|  5π |

|  10π |

|  25π |

| |

|12.[pic] |

|In the diagram of [pic]ABC, [pic][pic][pic], AB = 12y, and CD = 8y.  The area of [pic]ABC can be expressed as |

|  96 y2 |

|  48 y2 |

|  24 y2 |

|  20 y2 |

| |

| |

|13.   |

|[pic] |

|In the diagram, ABCD is a trapezoid with bases [pic] and [pic]. [pic] is perpendicular to [pic], and [pic] is a diameter of |

|semicircle O. AB = 16, BC = 17, ED = 14, and BE = 20. |

|(a) AE = [pic]. |

|(b)  The area of the entire figure, to the nearest tenth, is [pic]square units. |

|[Note: Use [pic]= 3.14.] |

| |

|14.A landscaper has two gardens: one is a square and the other is a rectangle. The width of the rectangular garden is 5 yards |

|less than a side of the square one, and the length of the rectangular garden is 3 yards more than a side of the square garden. |

|If the sum of the areas of both gardens is 165 square yards, find the measure of a side of the square garden. |

|The side is [pic]yards. |

| |

|15.If the lengths of the sides of a triangle are represented by 3x, 2x [pic]1, and 3x + 2, express the perimeter of the triangle|

|as a binomial in terms of x. |

|  7x2 [pic]x |

|  18x3 + 3x2 [pic]6x |

|  8x  + 1 |

|  7x [pic]1 |

| |

|16.The radius of a circle is 7. What is the area of the circle in terms of π? |

|  7π |

|  7π2 |

|  14π |

|  49π |

| |

|17.Find the area of a right triangle whose legs have lengths 6 and 8. |

|  10 |

|  14 |

|  24 |

|  28 |

| |

|18.The diameter of a circle is 8. What is the area of the circle in terms of  [pic]? |

|  8[pic] |

|  16[pic] |

|  64[pic] |

|  8[pic]2 |

| |

|19.If each side of square is doubled, the area of the square |

|  remains the same |

|  is divided by 2 |

|  is doubled |

|  is multiplied by 4 |

| |

| |

|20.   |

|[pic] |

|In the diagram, ABCD is a rectangle with E a point on [pic], EC = 5, BE = 13, and AB = 20. |

|The area of trapezoid ABED is [pic]square units. |

| |

|21.If the length of any rectangle is increased by 2 and the width is unchanged, the perimeter is |

|  increased by 2 |

|  multiplied by 2 |

|  increased by 4 |

|  multiplied by 4 |

| |

|22.The area of a circle is represented by 16[pic]. What is the length of a diameter of the circle? |

|16 |

|8 |

|4[pic] |

|4 |

| |

|23.The perimeter of a parallelogram is 32 meters and the two shorter sides each measure 4 meters. What is the length of each of |

|the longer sides? |

|  4  meters |

|  6  meters |

|10 meters |

|12 meters |

| |

|24.If the length of a rectangle is represented by 20a and the width is represented by 0.4a, the area of the rectangle is |

|represented by |

|  50a |

|  80a2 |

|  20.4a2 |

|  8a2 |

| |

|25.What is the circumference of a circle whose area is 16[pic]? |

|  64[pic] |

|  32[pic] |

|  8[pic] |

|  4[pic] |

| |

|[pic] |

|26.In the diagram, right triangle ABC is inscribed in a circle, BA is a diameter, BC = 6 centimeters, and AC = 8 centimeters.  |

|Using the approximation [pic][pic]3.14, the area of the shaded portion to the nearest tenth of a square centimeter, is |

|[pic]square centimeters. |

| |

|27.What is the diameter of a circle whose circumference is 5? |

|[pic] |

|[pic] |

|[pic] |

|[pic] |

| |

|28.Kerry is planning a rectangular garden that has dimensions of 4 feet by 6 feet. Kerry wants one-half of the garden to have |

|roses, and she says that the rose plot will have dimensions of 2 feet by 3 feet. Is Kerry correct? |

|yes |

|no |

| |

|29.If the circumference of a circle is 10[pic] inches, what is the area, in square inches, of the circle? |

|10[pic] |

|25[pic] |

|50[pic] |

|100[pic] |

| |

|30.Keesha wants to tile the floor shown in the accompanying diagram. |

|[pic] |

|  |

|If each tile measures 1 foot by 1 foot and costs $2.99, what will be the total cost, including an 8% sales tax, for tiling the |

|floor? Round your answer to the nearest cent. |

|$[pic] |

| |

|31.In the accompanying diagram, a circle with radius 4 is inscribed in a square. |

|[pic] |

|  |

|What is the area of the shaded region? |

|64 - 16[pic] |

|16 - 16[pic] |

|64 - 8[pic] |

|16 - 8[pic] |

| |

|32.What is the approximate circumference of a circle with radius 3? |

|7.07 |

|9.42 |

|18.85 |

|28.27 |

| |

|33.If the circumference of a circle is doubled, the diameter of the circle |

|remains the same |

|increases by 2 |

|is multiplied by 4 |

|is doubled |

| |

|34.Mr. Petri has a rectangular plot of land with length = 20 feet and width = 10 feet. He wants to design a flower garden in the|

|shape of a circle with two semicircles at each end of the center circle, as shown in the accompanying diagram. He will fill in |

|the shaded area with wood chips. If one bag of wood chips covers 5 square feet, how many bags must he buy? |

|[pic] |

| |

| |

|35.A dog is tied with a rope to a stake in the ground. The length of the rope is 5 yards. What is the area, in square yards, in |

|which the dog can roam? |

|25[pic] |

|10[pic] |

|25 |

|20 |

| |

|VOLUME & SURFACE AREA |

| |

|1.A side of a cube measures 4 centimeters and a side of a smaller cube measures 2 centimeters. The volume of the larger cube is |

|how many times the volume of the smaller cube? |

|  6 |

|  2 |

|  8 |

|  4 |

| |

|2.The volume of a rectangular solid is 180 cubic centimeters. The length is 10 centimeters, and the width is 4 centimeters. |

|Using the formula V = lwh, calculate the height. |

|  4.5 centimeters |

|  45 centimeters |

|  72 centimeters |

|  7200 centimeters |

| |

|3.If the length of the edge of a cube is 5x, the volume of the cube is |

|  5x3 |

|  15x3 |

|  125x3 |

|  625x3 |

| |

| |

|4.  _________ |

|[pic] |

|Jed bought a generator that will run for 2 hours on a liter of gas. The diagram shows the gas tank on the generator as a |

|rectangular prism with dimensions 20 cm by 15 cm by 10 cm. If Jed fills the tank with gas, how long will the generator run? |

|  1.5 hours |

|  2 hours |

|  3 hours |

|  6 hours |

| |

|5.The volume of a rectangular solid is 80 cubic centimeters, the length is 2 centimeters, and the width is 4 centimeters. What |

|is the height of the rectangular solid? |

|  5 centimeters |

|  6 centimeters |

|  10 centimeters |

|  20 centimeters |

| |

|6.A right circular cylinder has a base whose area is 12[pic]. If the height of the cylinder is 6, the volume of the cylinder is |

|  18[pic] |

|  24[pic] |

|  36[pic] |

|  72[pic] |

| |

| |

|7.  _________ |

|[pic] |

|A roll of candy is shown in the accompanying diagram.  The shape of the candy is best described as a |

|  rectangular solid |

|  pyramid |

|  cone |

|  cylinder |

| |

|8.The volume of a cube is 64 cubic inches. Its total surface area, in square inches, is |

|16 |

|48 |

|96 |

|576 |

| |

|9.The volume of a rectangular pool is 1,080 cubic meters.  Its length, width, and depth are in the ratio 10:4:1.  Find the |

|number of meters in each of the three dimensions of the pool. |

|length = [pic]meters, width = [pic]meters, depth = [pic]meters |

| |

|10.If the length of a rectangular prism is doubled, its width is tripled, and its height remains the same, what is the volume of|

|the new rectangular prism? |

|double the original volume |

|triple the original volume |

|six times the original volume |

|nine times the original volume |

| |

|11.In the diagram, a rectangular container with the dimensions 10 inches by 15 inches by 20 inches is to be filled with water, |

|using a cylindrical cup whose radius is 2 inches and whose height is 5 inches. |

|[pic]  |

|What is the maximum number of full cups of water that can be placed into the container without the water overflowing the |

|container? |

|[pic]cups |

| |

|12.A fish tank with a rectangular base has a volume of 3,360 cubic inches. The length and width of the tank are 14 inches and 12|

|inches, respectively. Find the height, in inches, of the tank. |

|height = [pic]inches |

| |

|13.A box in the shape of a cube has a volume of 64 cubic inches. What is the length of a side of the box? |

|[pic]in |

|16 in |

|8 in |

|4 in |

| |

|14.Which diagram represents the figure with the greatest volume? |

|[pic] |

| |

|15.As shown in the accompanying diagram, the length, width, and height of Richard's fish tank are 24 inches, 16 inches, and 18 |

|inches, respectively. Richard is filling his fish tank with water from a hose at the rate of 500 cubic inches per minute. How |

|long will it take, to the nearest minute, to fill the tank to a depth of 15 inches? |

|[pic] |

|Answer: [pic]minutes |

|  |

| |

|16.A storage container in the shape of a right circular cylinder is shown in the accompanying diagram. |

|[pic] |

|What is the volume of this container, to the nearest hundredth? |

|56.55 in3 |

|125.66 in3 |

|251.33 in3 |

|502.65 in3 |

| |

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