Mathematics, 12.03.2020 02:10 savannahsharp5149
Manuel bought a balloon (that is a perfect sphere) with a radius of 2 cm. He wanted his balloon to be bigger, so he blew 2 big breaths of air into the balloon. Each big breath increased the balloon's radius by 1 cm. What is the ratio of the current volume of the balloon to the original volume of the balloon?
Options
(A) 1/8
(B) 1/4
(C) 4
(D) 8
Answers: 2
![\bf \textit{volume of a sphere, \underline{originally}}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r = 2 \end{cases}\implies V=\cfrac{4\pi (2)^3}{3}\implies V=\cfrac{32\pi }{3} \\\\\\ \textit{volume of a sphere, \underline{later on}}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r = 4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V=\cfrac{256\pi }{3} \\\\[-0.35em] ~\dotfill](/tpl/images/0544/0964/79b2d.png)
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Manuel bought a balloon (that is a perfect sphere) with a radius of 2 cm. He wanted his balloon to b...
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