Volume of Cones, Cylinders, and Spheres

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height.

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Front

What is the formula for the volume of a sphere?

Back

The volume V of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Front

How do you find the radius of a cone if the diameter is given?

Back

The radius r is half of the diameter. If the diameter d is given, then r = d/2.

Front

If a cone has a height of 3 feet and a diameter of 8 feet, what is its radius?

Back

The radius is 4 feet (since the diameter is 8 feet, r = 8/2 = 4 feet).

Front

Calculate the volume of a cone with a radius of 4 feet and a height of 3 feet.

Back

The volume is 50.27 ft³ (V = (1/3)π(4)²(3) = 50.27 ft³).

Front

What is the difference between the volume of a cone and a cylinder with the same base and height?

Back

The volume of a cone is one-third that of a cylinder with the same base and height.

Front

What is the volume of a cylinder with a radius of 5 feet and a height of 10 feet?

Back

The volume is 785.4 ft³ (V = π(5)²(10) = 785.4 ft³).

Front

What is the volume of a sphere with a radius of 6 feet?

Back

The volume is 904.32 ft³ (V = (4/3)π(6)³ = 904.32 ft³).

Front

If the radius of a sphere is doubled, how does its volume change?

Back

If the radius is doubled, the volume increases by a factor of 8 (since volume is proportional to the cube of the radius).