Lesson 17 ~ Volume of Prisms
Name__________________________________________
Period______
Date____________
1. An octagonal swimming pool has a base area of 42 square meters. The pool is 3 feet deep. Find
the volume of the pool.
2. A fish aquarium is a rectangular prism. It is 18 inches long, 12 inches wide and 14 inches tall.
What is the volume of the aquarium?
Find the volume of each prism.
3.
4.
5.
1 in
8 cm
2 yd
3 yd
14 in
2.5 in
10 yd
7 cm
4 cm
6. A water pitcher is a hexagonal prism. It is 32 cm tall. The area of the base is 93 cm².
a. Sketch and label a diagram of the water pitcher.
b. Calculate the volume of the pitcher.
7. Siri is grocery shopping. She is buying macaroni. One box is 6 inches long, 1 inch wide and 9
inches tall. The second box is 3 inches long, 3 inches wide and 6 inches tall.
a. The Oregon State Assessment formula sheet gives the formula, V = lwh for volume of a
rectangular prism. Use this formula to find the volume of each box of macaroni.
b. Which box has a larger volume?
©2008 SMC Curriculum
Oregon Focus on Surface Area and Volume
Lesson 18 ~ Volume of Cylinders
Name__________________________________________
Period______
Date____________
Find the volume of each cylinder. Use 3.14 for π. Round answers to the nearest hundredth, if
needed.
1.
2.
3.
4 ft
3.5 cm
18 m
5 ft
30 m
11.2 cm
4. Sumo-Sumo Gas Company has a tanker-truck for hauling gasoline. The cylindrical tank has a
diameter of 5.4 meters. The tank is 16 meters long. How many cubic meters of gas can the truck
haul?
5. Rita has a circular hot tub. The hot tub has a circumference of 25.12 feet. It is 3.5 feet deep.
a. Find the radius of the hot tub. Use 3.14 for π.
b. How much water can the tub hold?
c. The hot tub manual recommends filling the hot tub 80% of its full capacity. How much
water should Rita put in the tub in order to follow the recommendation?
Find each missing measure. Use 3.14 for π, if necessary.
6. Volume = 282.6 ft³
7. V = 12.56 cm³
Area of the base = ________
Height = ________
2 cm
10 ft
h
8. A cylindrical bucket can hold approximately 301.44 in³. The base of the bucket is 50.22 in².
What is the height of the bucket to the nearest inch?
©2008 SMC Curriculum
Oregon Focus on Surface Area and Volume
Lesson 19 ~ Volume of a Sector of a Cylinder
Name__________________________________________
Period______
Date____________
1. A cylinder has a volume of 120 cubic meters.
a. Find the volume of a sector with a 75° central angle.
b. Find the volume of a sector with a 300° central angle.
2. A cylinder has a radius of 8 inches and is 14 inches tall. Find the volume of a 90° slice of the
cylinder. Use 3.14 for π.
Find the volume of each sector. Use 3.14 for π.
3.
6 ft
4.
10 ft
5 cm
36°
14 cm
5. A horizontal pipe is used to drain water from a parking lot. The pipe is 4 inches wide and it is 10
feet long. Find the volume of the water when the pipe is filled to its diameter. Use 3.14 for π.
6. A holding tank is the shape of a cylinder and is divided into two parts. One sector is 165° and the
other sector is 195°. The radius of the holding tank is 12 ft. The tank is 40 ft tall. Use 3.14 for π.
a. Find the volume of the whole cylinder.
b. What is the volume of the small sector of the tank?
c. What is the volume of the large sector of the tank?
d. Add part b and part c. What do you notice about this sum and the answer in part a?
Explain.
7. Carlos makes pizza. Each slice of pizza has a volume of 12.4 in². Each slice of pizza has a
central angle of 30°. Find the volume of a whole pizza. Use 3.14 for π.
©2008 SMC Curriculum
Oregon Focus on Surface Area and Volume
Lesson 20 ~ Volume of Pyramids
Name__________________________________________
Period______
Date____________
1. The volume of a pyramid is 50 mm 3 . What is the volume of a prism that has a congruent base
and is the same height as the pyramid?
2. A prism can hold 45 gallons of water. How many gallons of water can a pyramid with the same
base and height hold?
Find the volume of each pyramid.
3.
4. Base area = 60 ft²
5. Pyramid height = 12.3 m
7 ft
12 m
5.2 m
5m
5m
7.5 m
6. A pyramid has a base that is 14 yd². It is 6 yards tall. What is the volume of the pyramid?
7. A safety marker is an octagonal pyramid. It is 4 feet tall. The base of the marker is 1 square
feet. Find the volume of the marker.
8. A square pyramid has a perimeter of 40 cm and it is 15 cm tall. Find the volume of the pyramid.
9. The volume of a pyramid is 47 m³. The height of the pyramid is 6 meters. What is the area of its
base?
10. Kipp constructed a pentagonal pyramid for his social studies report. The base had an area of
12 cm². It took 48 cubic centimeters of clay to make his model. Find the height of the pyramid.
©2008 SMC Curriculum
Oregon Focus on Surface Area and Volume
Lesson 21 ~ Volume of Cones
Name__________________________________________
Period______
Date____________
Find the volume of each cone. Use 3.14 for π.
1.
2.
3.
8.5 m
4 in
13.2 m
12.7 m
9m
15 in
15.7 m
9m
4. A cone has a radius of 3 yards and height of 3.5 yards.
a. Find the volume of the cone.
b. Find the volume of a cylinder with the same radius and height as the cone.
5. A snow cone cup is 12 cm tall and has a diameter of 8 cm. Find the volume of flavored ice that
can be held inside the snow cone cup.
6. A cement truck malfunctioned causing all of the cement to be dumped all at one time. The pile of
cement was in the shape of a cone. It had a radius of 12 feet and a height of 2 feet. How much
cement had been spilled?
Find each missing measure. Use 3.14 for π.
7. Volume = 980 mm³
Area of the base = ________
14 mm
8. Volume = 15.7 ft³
Height of the cone = ________
h
1 ft
9. A conveyor belt dumps gravel into conical piles. Kevin calculated the area of the base of one pile
of gravel to be 22 square feet. The volume of pile is 77 cubic feet. Find the height of the pile.
©2008 SMC Curriculum
Oregon Focus on Surface Area and Volume
Lesson 22 ~ Volume of Composite Solids
Name__________________________________________
Period______
Find the volume of each composite solid. Use 3.14 for π.
1.
2.
10 ft
Date____________
3m
10 ft
14 ft
4 ft
5m
8m
8m
5 ft
20 ft
3.
4. A square prism with a cylinder removed.
4.2 m
2 cm
2.5 m
8 cm
11.6 m
8 cm
8 cm
5. A 26 m tall barn is an octagonal prism with an octagonal pyramid on top of it. The area of the
octagon is 62.5 m². The cylindrical part of the barn is 18.5 m tall. The pyramidal top is 7.5 m
tall. What is the volume of the barn?
6. A storage company claims that each unit has 315 cubic feet
of storage room available. A diagram of a one unit is to the right.
Determine if their claim is accurate.
2 ft
7 ft
8 ft
5 ft
C
©2008 SM Curriculum
Oregon Focus on Surface Area and Volume
Lesson 23 ~ Similar Solids
Name__________________________________________
Period______
Date____________
Determine if each pair of solids is similar. If a pair of figure is similar, identify the scale factor.
1.
2.
16
8
15
5
24
6
12
2
4
18
3. The scale factor between Solid A and Solid B is 3 : 7. Identify their area ratio.
4. The scale factor between Solid T and Solid Y is 1 : 5. Identify their volume ratio.
5. The volume ratio between two similar cylinders is a³ : b³. What is the scale factor between the
two cylinders?
6. Two similar prisms have a scale factor of 2 : 3. The small prism has a volume of 250 mm³. Find
the volume of the large prism.
7. A large baking sheet has an area of 432 in². A small baking sheet is similar to the large one. The
ratio of their lengths is 2 : 1. Find the area of the small baking sheet.
8. Two cylinders have a scale factor of 5 : 2. The surface area of the small cylinder is 6.28 square
feet. Find the surface area of the large cylinder
9. The volume ratio between two similar prisms is 4³: 5³.
a. Identify their scale factor.
b. Identify their linear ratio.
c. Identify their area ratio.
d. The volume of the large prism is 875 cubic units. Find the volume of the small prism.
©2008 SMC Curriculum
Oregon Focus on Surface Area and Volume