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45 votes
FIND THE RADIUS OF THE SHPERE WITH THE GIVEN VOLUME?
562.5π in.³

User Tacoshy
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1 Answer

15 votes
15 votes

Answer:

  • Radius = 7.5 in

Explanation:

In the question we have given volume of Sphere that is 562.5 π in³ and we have asked to find the radius of given sphere. We know that the volume of sphere ,


\blue{ \boxed{ \rm{Volume \: of \: Sphere = (4)/(3) \pi r {}^(3) }}}

So equating it with given volume for finding the radius of sphere :


\longmapsto \: (4)/(3) \pi r{}^(3) = 562.5\pi

Step 1 : Cancelling π as it was present in both side :


\longmapsto\:(4)/(3) \cancel{\pi }r{}^(3) = 562.5 \cancel{\pi}

Step 2 : Transposing 4/3 to right hand side :


\longmapsto \: r {}^(3) = 562.5 * (3)/(4)

Step 3 : Multiplying 562.5 with 3 :


\longmapsto \:r {}^(3) = (1687.5)/(4)

Step 4 : Dividing 1687.5 by 4 :


\longmapsto \:r {}^(3) = 421.875

Step 5 : Finding cube root of 421.875


\longmapsto \:r = \sqrt[3]{421.875}

Step 6 : We get :


\longmapsto \: \red{ \boxed{r = 7.5}}

  • Therefore , radius of sphere is 7.5 inches .

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User Rowan Freeman
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