Cylinder
Cone
Sphere
Similar Solids
Surface Area and Volume of Similar Solids
100
State the formula for finding the volume of a cylinder.
What is V = Bh
or
100
State the formula for finding the volume of a cone.
What is V = 
100
State the formula for finding the volume of a sphere.
What is V = 
100
Complete the statement:
Two solids are similar if their corresponding linear measures/dimensions are _______________.
in proportion
100
Two similar solids have corresponding linear measures that are in the ratio below. What are the ratios for their surface areas and volumes?
Surface Area:
Volume:
200
Find the volume. Round to the nearest tenth, if necessary.
What is approximately 62.8 cm3?
200
Find the volume. Round to the nearest hundredth, if necessary.
What is approximately 150.72 ft3?
200
A sphere has a radius of 3 meters. Find the volume. If necessary, round to the nearest hundredth.
What is approximately 113.04 meters3?
200
Cylinder A and Cylinder B have the dimensions below. Are the cylinders similar? Explain and provide math evidence.
Cylinder A: radius = 7 yd; height = 10 yd
Cylinder B: radius = 2 yd; height = 6 yd
The cylinders are NOT similar because the radius ratio and height ratio do not form a proportion. (The cross products are not equal.)
200
Two similar solids have surface areas that are in the ratio below. What are the ratios for their corresponding linear measures and volumes?
Corresponding linear measures:
Volumes:
300
Francisco is making an effort to drink more water, and has set a goal of 2 liters per day. He wants to know the volume of the water bottle he takes to school each day. The diameter of the bottle is 8 cm and the height is 20 cm. Find the volume. Round to the nearest tenth, if necessary.
What is approximately 1004.8 cm3?
300
Find the volume. If necessary, round to the nearest hundredth.
What is approximately 12.56 ft3?
300
Find the volume of a sphere with a diameter of 13 meters. If necessary, round to the nearest tenth.
What is approximately 1,149.8 cubic meters?
300
Prism A and Prism B are similar. Find the missing dimensions and provide math evidence.
Prsim A: ___ ft length, 3 ft width, 6 ft height
Prism B: 8 ft length, 6 ft width, ___ ft height
What are 4 ft length for Prism A and 12 ft height for Prism B?
300
The cones are similar. Write and solve a proportion to find the surface area of Cone B. If necessary, round to the nearest tenth.
Cone A: radius = 3 cm; SA = 75 cm2
Cone B: radius = 2 cm; SA = ____
What is approximately 33.3 square cm?
400
A log has a volume of 32,000 in3. The diameter of the log is 32 inches. Find the height of the log. Round to the nearest hundredth, if necessary.
What is approximately 39.81 inches?
400
A cone has a radius of 5.5 cm and an approximate volume of 538.3 cubic centimeters. Find the height to the nearest whole number.
What is approximately 17 cm?
400
Find the volume of a hemisphere that has a diameter of 10 inches. If necessary, round to the nearest hundredth.
What is approximately 261.67 cubic inches?
400
Cone A and Cone B have the dimensions below. Are the cones similar? Explain and provide math evidence.
Cone A: radius = 4 mm; slant height = 12 mm
Cone B: diameter = 6 mm; slant height = 9 mm
The cones are similar because the ratios are proportional (cross-products are equal).
400
The cones are similar. Write and solve a proportion to find the volume of Cone A. If necessary, round to the nearest tenth.
Cone A: height = 5 cm; V = ____
Cone B: height = 9 cm; V = 288 cm3
What is approximately 49.4 cm3?
500
A tank on a road roller is filled with water to make the roller heavy. The tank is a cylinder that has a height of 6 feet and a radius of 2 feet. One cubic foot of water weighs 62.5 pounds. Find the weight of the water in the tank. If necessary, round to the nearest pound.
What is approximately 4710 pounds?
500
The volume of a cone with a height of 5 m is 20.9 m3. Find the radius to the nearest tenth.
What is approximately 2.0 m?
500
A sphere has a volume of 905 cubic inches. Find the radius of the sphere to the nearest whole number.
What is approximately 6 inches?
500
Cone A and Cone B are similar. Find the missing dimensions and provide math evidence.
Cone A: 5 in. radius, __ in. height, 13 in. slant height
Cone B: __ in. radius, , 36 in. height, 39 in. slant height
What are 15 in. radius for Cone B and 12 in. height for Cone A?
500
The prisms are similar. The surface area and volume of the small prism are given below. Find the surface area AND volume of the large prism. If necessary, round to the nearest tenth.
Small Surface Area= 122 square feet
Small Volume = 84 cubic feet
The surface area is approximately 358.5 square feet.
The volume is approximately 423.2 cubic feet.