Name ______________________________ Date ... - Geometry Unit
Name ________________________________________ Date ____________________
Volume Formula – Rectangular Prisms
I. Find the volume of the following rectangular prisms.
1.
|Length (l) |Width (w) |Height (h) |Process Column |Volume |
| | | | |(in cubic units) |
| | | | | |
2.
|Length (l) |Width (w) |Height (h) |Process Column |Volume |
| | | | |(in cubic units) |
| | | | | |
Volume Formula: ____________________
2)
II. Find the area of each base from above.
a.) b.) c.)
3. How did you figure out the area of the base of your prisms?
4. Is the area of each base the same as the volume of each prism? Yes or No? Explain.
5. What is the volume of each prism from above?
a.) b.) c.)
III. Calculate the volume of each rectangular prism.
Volume Formula: ______________
Volume Formula: ______________
7)
8. A tunnel is being built through a small hill. It will be 10 ft tall and 15 ft wide. A diagram of
the tunnel is shown below.
Which of the following is the best estimate of the volume of the tunnel?
A. 9000 ft[pic] B. 4000 ft[pic] C. 6000 ft[pic] D. 9000 ft[pic]
9. Matt’s aquarium is shaped like a rectangular prism. The base of his tank has an area of
59.8 square feet. If the water level is at a height of 9 feet, what is the volume of the water
in the tank?
A. 68.8 cu. ft. B. 538.2 cu. ft. C. 518.2 cu. ft. D. 1076.4 cu. ft.
Developing Volume Formula – Triangular Prisms
I. Area of Triangles Review
10. Find the area for each triangle below:
Formula for Area of a Triangle: _______________
Answer ___________ Answer ___________ Answer ___________
11. Which components of a triangular prism make-up the base of the prism?
12. How can you distinguish between the height of a triangular prism and height of the base of
the prism?
II. Volume of Triangular Prisms
Formula for area of the base of a triangular prism:
13.
14.
15. A camping tent has the shape of the triangular prism below. What is the size of the tent in
cubic feet?
16. A triangular prism has a volume of 100cm[pic] and a height of 25cm. Find the area of its base.
17. A rectangular box has a volume of 8856 cm[pic]. The length of the box is 24.6 cm. The
width of the box is 18 cm. Find the height.
18. The volume of a cylinder is 15,700 cm[pic]. The area of the base is 628 cm[pic]. What is the
height?
19. The volume of a cylinder is 3.14 m[pic]. Its height is 1 m. Find the radius and diameter of the
cylinder.
Radius _______ Diameter _____
20. A cube has a volume of 64 cubic centimeters. What is the length of each edge of the
cube?
21. A watering trough for horses has the shape of the triangular prism below. How much
water will the trough hold?
22. The sand level in the sandbox is 4 inches below the top of the sandbox. The bottom of
the box takes 1728 square inches of space. The height of the sandbox is 12 inches.
Which process below could be used to calculate the volume of the sand?
A. [pic] V = 1728 + 12 C. V = 1728 [pic] 4 [pic]12
B. V = (1728)(12) D. V = 1728 (12 - 4)
-----------------------
Review of 6th Grade Skills
3 cm
3 cm
3 cm
5 cm
3 cm
4 cm
4 cm
6 cm
1.5 cm
a.)
4 cm
b.)
c.)
2 cm
1 cm
4 cm
3 cm
10 cm
To calculate the volume of a rectangular prism, you can use:
V = _________ or
V = _________
6.
|Area of Base (B) |Height of Prism (h) |Process |Volume |
| | |Column |(in cubic units) |
| | | | |
Base area = 24 in2
Height = 2 in
Explain 3 ways to find the volume of this prism:
a.)
b.)
c.)
60 ft
3 feet
8 feet
4 ft
5 ft
4 ft
2 ft
[pic]
Base area = 24 in2
Height = 2.5 in
|Area |Height |Process |Volume |
|of Base (B) |of Prism (h) |Column |(in cubic units) |
| | | | |
[pic]
b =6 cm
h =2 cm
h =4 cm
|Area |Height |Process |Volume |
|of Base (B) |of Prism (h) |Column |(in cubic units) |
| | | | |
12 ft
4[pic] ft
5 ft
A. 135 ft[pic] C. 21.5 ft[pic]
B. 270 ft[pic] D. 135 ft[pic]
A. 75 cm[pic] C. 125cm[pic]
B. 4 cm[pic] D. 25 cm[pic]
3 ft
A. 48 ft[pic] C. 86 ft[pic]
B. 96 ft[pic] D. 192 ft[pic]
4 ft
8 ft
12 in.
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