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?

Respuesta :

The beach balls are spherical.

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

Therefore

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

The diameter of the giant beach ball can be found below

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