Question

The image shows three tennis balls enclosed in a cylindrical can. Choose all that are correct. The volume of a single tennis ball is 14.14 in3. The volume of the can is 56.55 in3. The empty space inside the can is 14.13 in3. The volume of three tennis balls is 42.42 in3.

Answer 1

The volume of a single tennis ball is
`14.14\ in^(3)`

The volume of three tennis balls is
`42.42\ in^(3)`

Explanation:

Step 1

Find the volume of a single tennis ball

we know that

The volume of a sphere is equal to

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

where r is the radius of the sphere

In this problem

`r=3/2=1.5\ in`

substitute

`V=(4)/(3)\pi (1.5)^(3)`

`V=14.14\ in^(3)`

Step 2

Find the volume of the can

we know that

the volume of the cylinder is equal to

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

where r is the radius of the cylinder

h is the height of the cylinder

in this problem we have

`r=3/2=1.5\ in`

`h=8.4\ in`

substitute

`V=\pi (1.5)^(2)(8.4)`

`V=59.38\ in^(3)`

Statement

case A) The volume of a single tennis ball is
`14.14\ in^(3)`

The statement is true

See the procedure in Step 1

case B) The volume of the can is
`56.55\ in^(3)`

The statement is false

The volume of the can is
`59.38\ in^(3)` --> see the procedure Step 2

case C) The empty space inside the can is
`14.13\ in^(3)`

The statement is false

To find the empty space subtract the volume of three tennis ball from the volume of the can

`59.38\ in^(3)-3*14.14\ in^(3)=16.96\ in^(3)`

case D) The volume of three tennis balls is
`42.42\ in^(3)`

The statement is true

To find the volume of three tennis balls multiply the volume of a single tennis ball by three

`14.14*3=42.42\ in^(3)`