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MCAS Math – Geometry/Measurement (Set 6): you can use a calculator. Show all your work. No work means no credit. Remember to draw pictures to help you solve these!
1. The diagram below shows a right rectangular prism that
is 7 inches wide, 12 inches long, and 4 inches high.
What is the volume, in cubic inches, of the prism?
A. 152 B. 184
C. 320 D. 336
2. Kevin used snowballs in the shape of a sphere to build a snowman. The radius of the largest snowball was 1.5 times the radius of the smallest snowball. How many times greater was the volume of the largest snowball than the volume of the smallest snowball?
A. 7.065 B. 6.28 C. 3.375 D.2.25
3. Rectangle ABCD is similar to rectangle EFGH.
• The length of each side of rectangle EFGH is 2.4 times the length of the corresponding side of rectangle ABCD.
• The perimeter of rectangle ABCD is 120 feet
What is the perimeter of rectangle EFGH?
A. 288 ft B. 345.6 ft C. 576 ft D.691.2 ft
4. Circle O is inscribed in square EFGH, as shown here.
The circumference of circle O is 20 centimeters. Which of
the following is closest to the perimeter of square EFGH?
A. 24 cm B. 25.5 cm
C. 27 cm D. 28.5 cm
5. What is h, the height of the triangle represented
here, if its area is 58.5 square centimeters?
A. 13 cm B. 18 cm
C. 26 cm D. 39 cm
6. A glass lampshade is in the shape of a right circular cone with radius, r, and slant height, [pic], as given here. r = 7.5 inches
[pic] = 12.5 inches
Which of the following is closest to the lateral surface area of the lampshade?
A. 236 sq. in B. 295 sq in. C. 412 sq in. D. 589 sq in.
7. How many square feet of carpeting are needed to
cover the floor of the room represented by the
drawing below? Note that the shaded region is to be
left uncovered to leave space for the construction of
a built-in trophy case with a rectangular base.
A. 125 sq ft. B. 243 sq ft.
C. 273 sq ft. D. 303 sq ft.
8. The trapezoid pictured below has the measurements shown.
Which measure is closest to the perimeter of the trapezoid?
A. 41 in B. 59 in
C. 64 in D. 66 in
9. What is the effect on the circumference of a circle if the circle's radius is doubled?
A. The circumference is multiplied by 2 B. The circumference is multiplied by 4.
C. The circumference is multiplied by 8. D. The circumference stays the same.
10. A glass containing water is in the shape of a right circular cylinder with a radius of 3 centimeters. The height of the water in the glass is 10 centimeters.
a. What is the volume of the water in the glass? Be sure to include units of measure in your answer. Show or explain how you obtained your answer.
b. Five spherical marbles of equal size are dropped into the glass. The water in the glass rises to a height of 11 centimeters. What is the increase in the volume of the contents of the glass? Be sure to include units of measure in your answer. Show or explain how you obtained your answer.
c. What is the volume of one of the marbles? Be sure to include units of measure in your answer. Show or explain how you obtained your answer.
d. What is the radius of one of the marbles? Be sure to include units of measure in your answer. Show or explain how you obtained your answer.
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