Chapter 12.6, Problem 5PSA

To determine

To calculate: The volume of gas which is needed to inflate the spherical balloon.

Answer to Problem 5PSA

The volume of gas needed to inflate the balloon is $523.599{\text{ ft}}^{\text{3}}.$

Explanation of Solution

Given information: The diameter of inflated spherical balloon $\left(d\right)=10\text{ ft}\text{.}$

Formula used:

Volume of sphere $(V)=\left(\frac{4}{3}\right)\pi r^3$ ………...(i)

where r = radius of sphere

Calculation:

Here required volume of gas is just same as the volume of sphere when its diameter $\left(d\right)=10\text{ ft}\text{.}$

Using $r=\frac{d}{2}=\frac{10}{2}=5\text{ ft}\text{.}$ in equation (i)

  $\begin{array}{l}V=\left(\frac{4}{3}\right)\times \pi \times 5^3{\text{ ft}}^{\text{3}}\\ V=523.599{\text{ ft}}^{\text{3}}\end{array}$

Hence, the required volume of gas needed to inflate the spherical balloon is $523.599{\text{ ft}}^{\text{3}}.$