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Find the total surface area of the sphere whose volume is equal to the volume of a cone having the radius 12cm and height 8cm.

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678.45 c m^{2}

547.61 c m^{2}

978.34 c m^{2}

456 c m^{2}

answer is B.

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Detailed Solution

Radius of the cone

(r)

= 12cm
Height of the cone

(h)

= 8cm
Volume of the cone

(V)

\frac{π r^{2} h}{3}

\frac{22}{7}

\times

12^{2}

\times

\frac{8}{3}

\frac{22}{7}

\times 12

\times

12

\times

\frac{8}{3}

\frac{25344}{21}

1206.85 c m^{2}

Now,
Volume of sphere = Volume of cone

\Rightarrow \frac{4 π R^{3}}{3} = 1206.85

\Rightarrow \frac{4}{3}

\frac{22}{7}

R^{3} = 1206.85

\Rightarrow \frac{88}{21} R^{3} = 1206.85

\Rightarrow R^{3} = \frac{1206.85}{88}

21

\Rightarrow R^{3} = 287.99

\Rightarrow R = \sqrt[3]{287.99}

\Rightarrow R = 6.6 cm

Therefore,
Surface Area of the sphere =

4 π R^{2}

4

\frac{22}{7}

{(6.6)}^{2}

4

\frac{22}{7}

6.6

6.6

547.61 c m^{2}

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