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A bucket is of the shape of a frustum. If the radii of the circular ends are $28$ cm and $7$ cm and the height is $45$ cm. Find the capacity of the bucket.

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48150 {cm}^{3}

48510 {cm}^{3}

48105 {cm}^{3}

48205 {cm}^{3}

answer is B.

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Detailed Solution

Given that,the radii of the circular ends are

28

cm and

7

cm and the height is

45

cm.
Let height of the bucket be h and radius of the bigger circular end,

r_{1} = 28 cm

and, radius of the smaller circular end,

r_{2} = 45 cm

.
Volume of bucket

V = \frac{π}{3} (r_{1}^{2} + r_{1} r_{2} + r_{2}^{2}) h

\Rightarrow V = \frac{22}{3 \times 7} [28^{2} + 28 \times 7 + 7^{2}] \times 45 c m^{3}

\Rightarrow V = \frac{22}{21} [784 + 196 + 49] \times 45 c m^{3}

\Rightarrow V = \frac{22}{21} \times 1029 \times 45 c m^{3}

\Rightarrow V = 48510 c m^{3}

Therefore, the volume is

48510 c m^{3}

.
Hence, the correct option is 2.

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