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Find the volume of the frustum cone whose base and top radius is $10$ cm and $2$ cm respectively. The height of the cone is $3$ cm. (Use $π = \frac{22}{7}$ ).

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369.36 c m^{3}

379.36 c m^{3}

389.36 c m^{3}

319.36 c m^{3}

answer is C.

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Detailed Solution

Given,
The frustum cone whose base radius (R)and top radius(r) is

10

cm and

2

cm respectively.
The height(h) of the cone is

3

cm.
Volume of frustum

(V) = \frac{1}{3} π (R^{2} + r^{2} + Rr) \times h

\Rightarrow V = \frac{1}{3} \times \frac{22}{7} (10^{2} + 2^{2} + 10 \times 2) \times 3

\Rightarrow V = \frac{22}{7} (100 + 4 + 20)

\Rightarrow V = \frac{22 \times 124}{7}

\Rightarrow V = 389.71

{cm}^{3}

Therefore, the volume of the frustum cone is

389.71 c m^{3}

.
Hence, the correct option is 3.

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