Question

The surface area of a beach ball is 144π in2. Find the volume of air the beach ball will hold when it is fully inflated

Answer 1

The answer is 288π in³ 
:)

Answer 2

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

Step-by-step 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 :-

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

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

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