2 Answers

Nguyen Tuan Anh · Answer 1 · 2018-01-26T05:48:10+0000

Answer:
$\text{Volume}=288\pi\ in^3$

Explanation:

Given: The surface area of a beach ball =
$144\pi\ in^2$

The surface area of sphere is given by :-

$\text{SA}=4\pi r^2\\\\\Rightarrow144\pi=4\pi\ r^2\\\\\Rightarrow\ r^2=36\\\\\Rightarrow\ r=6\ in$

We know that the volume of a sphere is given by :-

$\text{Volume}=(4)/(3)\pi\ r^3$ , where r is the radius of the sphere.

$\Rightarrow\text{Volume}=(4)/(3)\pi (6)^3\\\\\Rightarrow\ \text{Volume}=288\pi\ in^3$

Hence, the volume of air the beach ball will hold when it is fully inflated is
$288\pi\ in^3$

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