Question

Three tennis balls are packaged in a cylindrical container as shown. The tennis balls touch the top and bottom of the canister and each other. (Use 3.14 for pi.) Round each answer to the nearest tenth.

A) Each tennis ball has a diameter of 2.6 inches.

What is the height of the cylinder? _____

B) Find the volume of one tennis ball.

Volume of one tennis ball= ____________

C) Find the volume of the cylinder.

Volume of cylinder = ______________

D) What is the volume of space in the cylinder not taken by the tennis balls?

Volume of unused space = ___________

Answer 1

Part A) The height of the cylinder is

Part B) The volume of one tennis ball is

Part C) The volume of the cylinder is

Part D) The volume of space in the cylinder not taken by the tennis balls is

Explanation:

Part A) Each tennis ball has a diameter of 2.6 inches

What is the height of the cylinder?

we know that

The height of the cylinder is equal to the diameter of one ball of tennis multiplied by 3

so

Part B) Find the volume of one tennis ball

The volume of the sphere (one tennis ball) is equal to

we have

----> the radius is half the diameter

substitute

Part C) Find the volume of the cylinder

The volume of the cylinder is equal to

we have

----> the radius is half the diameter

substitute

Part D) What is the volume of space in the cylinder not taken by the tennis balls?

we know that

The volume of space in the cylinder not taken by the tennis balls, is equal to the difference from the volume of the cylinder and the volume of three ball of tennis

Explanation:

Answer 2

Part A) The height of the cylinder is
`7.8\ in`

Part B) The volume of one tennis ball is
`9.2\ in^(3)`

Part C) The volume of the cylinder is
`41.4\ in^(3)`

Part D) The volume of space in the cylinder not taken by the tennis balls is
`13.8\ in^(3)`

Explanation:

Part A) Each tennis ball has a diameter of 2.6 inches

What is the height of the cylinder?

we know that

The height of the cylinder is equal to the diameter of one ball of tennis multiplied by 3

so

`h=2.6*3=7.8\ in`

Part B) Find the volume of one tennis ball

The volume of the sphere (one tennis ball) is equal to

`V=(4)/(3)\pi r^(3)`

we have

`r=2.6/2=1.3\ in` ----> the radius is half the diameter

`\pi=3.14`

substitute

`V=(4)/(3)(3.14)(1.3)^(3)`

`V=9.2\ in^(3)`

Part C) Find the volume of the cylinder

The volume of the cylinder is equal to

`V=\pi r^(2) h`

we have

`r=2.6/2=1.3\ in` ----> the radius is half the diameter

`\pi=3.14`

`h=2.6*3=7.8\ in`

substitute

`V=(3.14)(1.3)^(2) (7.8)`

`V=41.4\ in^(3)`

Part D) What is the volume of space in the cylinder not taken by the tennis balls?

we know that

The volume of space in the cylinder not taken by the tennis balls, is equal to the difference from the volume of the cylinder and the volume of three ball of tennis

`V=41.4-(3)*(9.2)=13.8\ in^(3)`