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The radius of a sphere is tripled. What happens to the volume?Hint: Test two scenarios and compare the volumes! Show your work. Used 3.14 for piC. It is 15 times largerD. It is 27 times largerA. It triplesB. It quadruples

User Pragya Mendiratta
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1 Answer

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12 votes

First, we need to test two scenarios using the sphere volume formula:

The volume for a sphere is given by:


A_s=(4)/(3)\pi r^3

Let us set r=3

Then:


\begin{gathered} A_(s)=(4)/(3)\pi r^(3) \\ A_s=(4)/(3)\pi(3)^3 \\ A_s=36\pi \\ A_s=113.04 \end{gathered}

If we tripled the radio= 3r = 3(3)= 9. Then:


\begin{gathered} A_s=(4)/(3)\pi(9)^3 \\ A_s=3052.08 \end{gathered}

Now, we need to compare both results:

A1 = 113.14

A2 = 3052.08

If we multiply A1 by 27=

27(113.14) = 3052.08

Hence, the volume when the radius is tripled is the product of the first volume by 27.

Therefore, the correct answer is option D.It is 27 times larger

User Flowoverstack
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