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A bucket of height 8 cm and made up of copper sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3 cm and 9 cm respectively. Calculate The height of the cone of which the bucket is a part, the volume of water which can be filled in the bucket and the area of copper sheet required to make the bucket,

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12 cm,

312 π {cm}^{3}

129 π {cm}^{3}

8 cm, 12 π {cm}^{3}, 19 π {cm}^{3}

4 cm, 412 π {cm}^{3}, 129 π {cm}^{3}

6 cm, 12 π {cm}^{3}, 19 π {cm}^{3}

answer is A.

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Detailed Solution

Given,
Height of bucket, (h) is 8 cm Lower radii of a cone,

r_{1} is 9 cm

Upper radii of a cone,

r_{2} is 3 cm

Suppose height of the cone=

h_{1}

\Rightarrow h_{1} = \frac{{hr}_{1}}{r_{1} - r_{2}}

\Rightarrow h_{1} = (\frac{8 \times 9}{9 - 3}) cm

= 12 cm

Now, volume of water that can be used to fill a bucket = The frustum's volume

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

= \frac{1}{3} π (9^{2} + 9 \times 3 + 3^{2}) \times 8 {cm}^{3}

= 312 π {cm}^{3}

Now, area of the required copper sheet to make the bucket

= π (r_{1} - r_{2}) 1 + π r_{2}^{2}

= π (9 - 3) + π \times 3^{2}

= 129 π {cm}^{2}

Hence ,12 cm height of the cone of which the bucket is a part,

312 π {cm}^{3}

, the volume of water which can be filled in the bucket and the area of copper sheet required to make the bucket is

129 π {cm}^{3}

.
Correct option is 1.

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