Geometry - Practice: Volume of Spheres

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 of the sphere.

Front

What is the volume of a sphere with a radius of 3 inches?

Back

V = (4/3)π(3)³ = 36π cubic inches.

Front

How do you convert cubic inches to cubic millimeters?

Back

1 cubic inch = 16,387.064 cubic millimeters.

Front

What is the volume of a sphere with a radius of 5 cm?

Back

V = (4/3)π(5)³ = 523.6 cubic cm.

Front

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

Back

The volume of a sphere increases with the cube of the radius; if the radius doubles, the volume increases by a factor of 8.

Front

What is the formula for the volume of a hemisphere?

Back

The volume V of a hemisphere is given by the formula V = (2/3)πr³, where r is the radius.

Front

If a sphere has a volume of 972π cubic inches, what is its radius?

Back

The radius r can be found using the formula V = (4/3)πr³. Solving for r gives r = 9 inches.

Front

What is the volume of a basketball with a radius of 4.7 inches?

Back

V = (4/3)π(4.7)³ ≈ 434.9 cubic inches.

Front

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

Back

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

Front

How do you find the volume of a sphere if you only know the circumference?

Back

Use the formula C = 2πr to find the radius r, then use V = (4/3)πr³ to find the volume.