Volume of Spheres, Cones, and Cylinders

Front

What is the formula for the volume of a sphere?

Back

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

Front

What is the formula for the volume of a cone?

Back

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

Front

What is the formula for the volume of a cylinder?

Back

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

Front

If a sphere has a radius of 3 inches, what is its volume?

Back

V = (4/3)π(3)³ = 36π ≈ 113.1 cubic inches.

Front

A cone has a radius of 4 cm and a height of 9 cm. What is its volume?

Back

V = (1/3)π(4)²(9) = 48π ≈ 150.8 cubic centimeters.

Front

What is the relationship between the radius and diameter of a sphere?

Back

The diameter of a sphere is twice the radius. (d = 2r)

Front

How do you find the height of a cylinder if you know its volume and base area?

Back

Use the formula h = V / A, where V is the volume and A is the area of the base.

Front

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

Back

V = π(5)²(10) = 250π ≈ 785.4 cubic meters.

Front

If the volume of a cone is 100 cubic inches and the height is 5 inches, what is the radius?

Back

Using V = (1/3)πr²h, we can solve for r: r = sqrt((3V)/(πh)) = sqrt((3*100)/(π*5)) ≈ 4.64 inches.

Front

What is the volume of a sphere with a diameter of 10 inches?

Back

First, find the radius: r = 10/2 = 5 inches. Then, V = (4/3)π(5)³ = (4/3)π(125) ≈ 523.6 cubic inches.