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A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $12$ m and height of the cone is $5$ m. Find the volume of the solid.

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1392 π m^{3}

4176 π m^{3}

1028 π m^{3}

1308 π m^{3}

answer is A.

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Detailed Solution

It is given a cone standing on a hemisphere with both their radii being equal to

12

m and height of the cone is

5

m.
Let, larger and smaller radius be R and r and height of the cone be h.
The volume of solid

=

volume of cone + volume of a hemisphere

\Rightarrow \frac{1}{3} π r^{2} h + \frac{2}{3} π r^{3}

\Rightarrow \frac{1}{3} π r^{2} (h + 2 r)

\Rightarrow \frac{1}{3} \times π \times 12 \times 12 (5 + 2 \times 12)

\Rightarrow \frac{1}{3} \times π \times 144 \times (5 + 24)

\Rightarrow \frac{1}{3} \times π \times 144 \times 29

\Rightarrow 1392 π m^{3}

Therefore, the volume of the solid

= 1392 π m^{3}

.
Hence, the correct option is 1.

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