Chapter 10 Review

Volume of Cylinders

100

Find the volume of a cylinder 

height= 16cm

diameter= 8cm

803.84 cm³

200

Find the volume of the cylinder

height= 10 ft

radius= 5ft

785 ft³

300

Find the radius of the cylinder

Volume= 28 m³

height= 4m

1.49 m

400

Find the height of the cylinder

Volume= 10,000 mm³

radius= 5 mm

h= 127.39 mm

500

A cylindrical hazardous waste container has a diameter of 1.5 feet and a height of 1.6 feet. About how many gallons of hazardous waste can the container hold? (1 ft³ ≈ 7.5 gal)

21.20 gal

Volume of Cones

100

Find the volume of the cone

height= 6 in

diameter= 4 in

25.12 in³

200

Find the volume of cone

height= 4 in

radius= 2 in 

16.75 in³

300

Find the height of the cone

Volume= 956 ft³

radius= 9ft

11.28 ft

400

Volume the radius of the cone

Volume= 183 cm³

height= 7cm

5.0 cm

500

A waterpark is building a new waterslide that funnels into a cone-shaped pool. The pool is 12ft deep with a radius of 10ft. Find the volume of the pool. How many gallons of water are needed to fill the pool?

1ft³=7.48 gallons

Volume= 1256ft³

9394.88 gallons

Volume of Spheres

100

Find the volume of the cone

radius= 6cm

904.32cm³

200

Find the volume of sphere

diameter=10ft

523.33ft³

300

Find the radius of the sphere

Volume= 14cm³

1.50 cm

400

Find the radius of the sphere

Volume =972 m³

6.15m

500

A company is designing a new water tank for a playground. The tank is made of two parts:

• A cylindrical base that is 12 feet tall with a radius of 4 feet
• A hemisphere (half of a sphere) sitting on top with the same radius of 4 feet
• What is the total volume of the water tank? 

736.8ft³

Surface Area of Similar Solids

100

Radius of cylinder A= 12ft

Height of cylinder A= 4ft

Radius of cylinder B=36ft

Height of cylinder B=12ft

Are the solids similar?

Yes

A/B=12/4=36/12=3ft

200

Cone X and Y are similar. The height of cone X is 13ft and the radius is 5ft. The radius of cone Y is 7 ft.

Find the height of cone Y. 

18.2ft

300

Prism A and B are similar. The height of prism A is 6cm. The height of prism B is 10cm. The surface area of prism B is 600cm².

What is the surface area of prism A?

216cm²

400

Pyramids G and H are similar. Pyramid G has a height of 90mm. Pyramid H has a height of 110mm.

What is the ratio of surface areas?

8100/12100=81/121mm²

500

Two similar rectangular gift boxes are made. The ratio of the lengths of the small box to the large box is 1 : 3.

The surface area of the small box is 54 square inches.

What is the surface area of the large box?

486in²

Volume of Similar Solids

100

Cones A and B are similar. The height of cone A is 5m and the height of cone B is 12m.

What is the ratio of volumes?

125/1728m³

200

Cylinder L and M are similar. The height of cylinder L is 3 ft with a volume of 3ft³. Cylinder M has a height of 10 ft.

What is the volume of cylinder M?

33.33ft³

300

Pyramid A has a height of 9ft and radius of 14ft. Pyramid B has a height of 11ft and a radius of 15ft. Pyramid C has a height of 29ft and a radius of 40ft. 

Which pyramids are similar?

Pyramids B and C

400

Cone V and W are similar. Height of cone V is 20cm. Height of cone W is 50cm. The volume of cone V is 190cm.

What is the volume of cone W?

2968.75 cm³

500

Cube Q and T are similar. Cube Q has a height of 2 yd. Cube T has a height of 4 yd. Surface area of cube Q is 13 yd² and a volume of 6 yd³.

What is the surface area and volume of cube T?

Surface area=52 yd²

Volume= 48 yd³