Sheet GQ3-34
Name:___________________________________________
Mr. Carman
1
Date:________________________
Focus: Prisms and Cylinders (Volume)
Do Now: (Review)
---------------------------------------------------------------------------------------------------------------------------1) How much water would you need to fill this tank?
5 in
4 in
12 in
2) How much water would you need to fill this tank?
7 in
13 in
24 in
3) These two tanks are called prisms because the top and bottom faces are congruent parallel
polygons.
4) To find the volume of a prism:
V = (Area of the base)(height)
Sheet GQ3-34
5) Draw a circle around each figure below that represents a prism. (Download this worksheet from
mrcarman.wikispaces.com for clearer images)
6) Think of prisms like toy blocks. If you make a stack of one type of prism, all of the blocks will line
up with their sides nice and neat.
7) Why isn’t a cylinder a prism?
2
Sheet GQ3-34
3
V = (area of the base)(height)
For these volume questions, using a picture will be necessary to receive credit.
8) A rectangular prism has a length of 9 units, and a width of 8 units. If the volume of the prism is 936
cubic units, what is the height of the prism?
9) A rectangular prism has a length of 11 units, and its volume is 704 cubic units. its width and height
are the same, find the remaining dimensions of the prism.
10) If this prism has a volume of 684 ft3, what is the area of its base?
12 ft
11)
Sheet GQ3-34
12) If the volume of a rectangular prism is 3x
x – 2, what is its width in terms of x?
3
9x2
4
30 x , and if its length is 3x, and its height is
13) Tim has a rectangular prism with a length of 10 centimeters, a width of 2 centimeters, and an
unknown height. He needs to build another rectangular prism with a length of 5 centimeters and
the same height as the original prism. The volume of the two prisms will be the same. Find the
width, in centimeters, of the new prism.
---------------------------------------------------------------------------------------------------------------------------14) How much water would we need to fill this fish tank? (2 decimal places)
6 cm
13 cm
Sheet GQ3-34
5
15) Find the volume of this can in terms of pi:
8 in
12 in
16) Find the volume of this can in terms of pi:
10 in
22 in
17) Find the volume of this can in terms of pi:
7 cm
13 cm
18) Find the volume of this cylinder in terms of pi:
101 mm
37 mm
19) The volume of a cylinder is 468
radius?
cubic inches. If the cylinder’s height is 13 inches, what is its
Sheet GQ3-34
20) The volume of a cylinder is 578.2
its radius?
cubic inches. If the cylinder’s height is 11.8 inches, what is
21) The volume of a cylinder is 225 cubic inches. If the cylinder’s diameter is 10 inches, what is the
height of the cylinder in terms of pi?
22) The volume of a cylinder is 1,377 cubic inches. If the cylinder’s diameter is 18 inches, what is the
height of the cylinder in terms of pi?
23) Find the volume of a rectangular prism whose length is 8, whose height is twice its width, and
whose width is 3 times its length.
6
Sheet GQ3-34
7
24) Find the volume of this rectangular prism in terms of x:
9x
x-7
x+5
25) The volume of a rectangular prism is 2,052 cubic cm. If its length is 18 cm, and its width is 6 cm,
find the height of the prism.
26) The volume of a rectangular prism is 2,349 cubic cm. If its width is 27 cm, and its height is 29 cm,
find the length of the prism.
27) In terms of x, what is the volume of a cube whose side measures 7x inches?
Sheet GQ3-34
8
28) Determine which popcorn container has a greater volume:
8.4 in
9.3 in
9.8 in
6.1 in
7.3 in
29) A can of soda is in the shape of a cylinder with a diameter of 6.4 cm and a height of 12.3 cm. How
many cubic cm of liquid does the can hold?
30) The volume of a cylinder is 128
the cylinder?
cubic inches. If the cylinder’s height is 8, what is the radius of
31) The volume of a cylinder is 162 cubic inches. If the cylinder’s diameter is 6 inches, what is the
height of the cylinder in terms of pi?
Sheet GQ3-34
9
32) The volume of a cylinder is 12,566.4 cm3. The height of the cylinder is 8 cm. Find the radius of the
cylinder to the nearest tenth of a centimeter.
33)
34) If the volume of a rectangular prism is 2 x
x + 4, what is its length in terms of x?
3
2x2
40 x , and if its width is 3x, and its height is
35) Tim has a rectangular prism with a length of 4 centimeters, a width of 6 centimeters, and an
unknown height. He needs to build another rectangular prism with a length of 8 centimeters and
the same height as the original prism. The volume of the two prisms will be the same. Find the
width, in centimeters, of the new prism.
***Remember, drawing a picture for each example is necessary to receive credit for this assignment.