Spheres and Cylinders

Volume

A sphere is made out of clay and is placed in a cylinder.

The diameter of the sphere is the same as the height and diameter of the cylinder.

Suppose the clay is flattened within the cylinder.

Suppose the height of the cylinder is 2 inches tall.

2 in

ches

What do you think is the height of the clay (X) and of the empty space (Y) created by the clay?

X

Y

X = 2 inches.

Y = 2 inches.

Find the volume of the cylinder and the sphere.

2 in

ches

43

h𝑖𝑛𝑐

23

h𝑖𝑛𝑐Volume of the Cylinder = 6.28 inches cubed

Volume of the Sphere = 4.1762 inches cubed

Remember:

The Volume of a Cylinder is V=Bh.

The Area of a Circle is A=.

Find the volume of the sphere using the volume formula. V=

2 in

ches

V=43𝜋 𝑟 3

V=43𝜋 (1 )3

V=43𝜋 (1 )

V=4.1762 (1 )4.1762 in3

What is the relationship between a cylinder and a sphere?

Practice

A playground ball has a diameter of 18 cm.

• Find the volume of the ball.

• If you created a cylinder that fits around the playground ball, find the volume and surface area of the cylinder.