Cubes
The formula for the volume of a cube with side length s.
What is V = s³?
The formula for the volume of a sphere with radius r.
What is V = 4/3πr³?
The formula for the volume of a cone with radius r and height h.
What is V = 1/3πr²h?
The formula for the volume of a cylinder with radius r and height h.
What is V = πr²h?
The general formula for the volume of any prism.
What is V = (area of base) × height?
If a cube has a side length of 5 cm, what is its volume?
What is 125 cm³?
A sphere has a radius of 6 cm. What is its volume?
What is 288π cm³? (or approximately 904.8 cm³)
A cone has a radius of 4 cm and a height of 9 cm. What is its volume?
What is 48π cm³? (or approximately 150.8 cm³)
A cylindrical water tank has a radius of 4 feet and a height of 10 feet. What is its volume?
What is 160π cubic feet? (or approximately 502.7 cubic feet)
A rectangular prism has dimensions 12 cm by 8 cm by 20 cm. What is its volume?
What is 1,920 cm³?
The volume of a cube is 27 cubic inches. What is the length of each edge?
What is 3 inches?
Based on the lab observation, how does the volume of a sphere compare to a cylinder with the same radius and height equal to the diameter?
What is 2/3 of the cylinder's volume?
Based on the lab observation, how does the volume of a cone compare to a cylinder with the same base and height?
What is 1/3 of the cylinder's volume?
If the radius of a cylinder is doubled while the height remains the same, by what number does the volume increase?
What is 4? (Since the radius is squared in the formula)
Based on the lab observation, how does the volume of a square-based pyramid compare to a cube with the same base and height?
What is 1/3 of the cube's volume?
If the volume of a cube increases by 8, by what number does the side length increase?
What is 2? (Because 2³ = 8)
The volume of a sphere is 36π cubic inches. What is its radius?
What is 3 inches? (Since 36π = 4/3π·r³, solving for r gives 3)
A decorative candle consists of a cylinder with a cone on top. The cylinder has radius 3 cm and height 5 cm, while the cone has the same base radius and height 7 cm. What is the total volume?
What is 45π + 21π = 66π cm³? (or approximately 207.3 cm³)
A cylindrical water tank holds 200π cubic meters of water. If the height is 8 meters, what is the radius of the base?
What is 5 meters? (Since 200π = πr²·8, solving for r gives 5)
A triangular prism has a right-angled triangular base with sides 3 cm, 4 cm, and 5 cm. If the prism is 10 cm tall, what is its volume?
What is 60 cm³?
A cube with a side length of 10 cm has a spherical hole with radius 3 cm drilled through its center. What is the remaining volume?
What is 1000 - 36π cm³? (or approximately 887 cm³)
A stone sculpture has a spherical hole with radius 3 cm carved in the center of a rectangular prism. The hole's volume is what fraction of a 12 cm by 8 cm by 20 cm rectangular prism?
What is 36π/1920 or approximately 0.059? (about 5.9%)
A cone with radius 6 cm and height 8 cm is filled with water. If the water is poured into a cylinder with radius 4 cm, what height will the water reach in the cylinder?
What is 6 cm? (Since πr₁²h₁/3 = πr₂²h₂, solving for h₂ gives 6)
A cylindrical tank with radius 6 cm is filled with water to a certain height. When 250π cm³ of water is removed, the water level drops by 7 cm. What was the original height of water in the tank?
What is 14 cm? (Since the volume removed is πr²h = π(6²)(7) = 250π, the water level dropped 7 cm from its original height of 14 cm)
A water tank is constructed from a rectangular prism with a triangular prism on top. The rectangular base measures 8 ft by 6 ft with a height of 10 ft. The triangular prism has the same 8 ft width as the rectangular base, a triangular height of 4 ft, and runs the full 6 ft length. What is the total volume of water the tank can hold?
What is 576 cubic feet?