Question

To the nearest tenth of a cubic inch, how much volume is added to a spherical balloon whose radius grows from 10 to 20 inches long?

A) 8245.7 in3
Eliminate
B) 17367.6 in3
C) 29321.5 in3
D) 41225.4 in3

Answer 1

`\bf \begin{array}{llll} \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=10 \end{cases} \\\\\\ V=\cfrac{4\pi 10^3}{3}\implies V=\cfrac{4000\pi }{3} \end{array}~\hfill \begin{array}{llll} \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=20 \end{cases} \\\\\\ V=\cfrac{4\pi 20^3}{3}\implies V=\cfrac{32000\pi }{3} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf \cfrac{32000\pi }{3}-\cfrac{4000\pi }{3}\implies \cfrac{32000\pi -4000\pi }{3}\implies \cfrac{28000\pi }{3}\qquad \approx\qquad 29321.5`