Question

A manufacturer makes solid rubber balls. It takes 111.3 cubic inches of rubber to make 3 equally sized balls. Rounding to the nearest hundredthof an inch, what is the diameter of one of the balls?

Answer 1

`4.55\text{ inches}`

Step-by-step explanation:

Here, we want to get the diameter of one of the balls

Firstly, we need to get the size of one of the balls

We can get this by dividing the total volume of the three balls by 3

Mathematically, we have this as:

`(111.3)/(3)\text{ = 37.1 cubic inches}`

To get the diameter of one of the balls, we can get the radius first and multiply the value by 2 since the diameter is 2 times the radius length

A ball is spherical in shape

The volume of a sphere is:

`\text{ V = }\pi r^3`

Thus:

`\begin{gathered} r^3=(37.1)/(\pi)^{}^{}^{} \\ \\ r\text{ = }\sqrt[3]{(37.1)/(\pi)} \\ \\ r\text{ = 2.277 in} \end{gathered}`

To get the diameter, we simply multiply this by 2

`\begin{gathered} d\text{ = 2r} \\ d\text{ = 2}*2.277\text{ in} \\ d\text{ = 4.55 in} \end{gathered}`