Question

6. Juliana's Beach Ball Company produces two sizes of beach balls. The small beach ball has a volume of905 in^3 and the giant size beach ball has a volume of 7,240 in^3 How many times longer is the diameterof the giant beach ball than the smaller beach ball?

Answer 1

The beach balls are spherical.

`\begin{gathered} \text{volume of the small beach ball=905 inches}^3 \\ ^{}\text{volume of the large beach ball 7}240inches^3 \end{gathered}`

Therefore

`\begin{gathered} \text{volume}=(4)/(3)\pi r^3 \\ r=(d)/(2) \\ \text{volume of the small ball=}(4)/(3)\pi r^3 \\ 905=(4)/(3)\pi((d)/(2))^3 \\ 905=(4)/(3)*\pi*(d^3)/(8) \\ 905=\frac{4\pi^{}d^3}{24} \\ 21720=4\pi d^3 \\ d^3=(21720)/(4\pi) \\ d^3=(5430)/(\pi) \\ d^3=\sqrt[3]{(5430)/(\pi)} \end{gathered}`

The diameter of the giant beach ball can be found below