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प्रश्न
The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.
उत्तर
Height of the bucket = 30 cm.
`r_1 = 21 cm`
`r_2 = 7 cm`
Therefore,
Capacity of the bucket
`=(pih)/3 [r_1^2 + r_1r_2 + r_2^2]`
`=22/7 xx 30/3 [(21)^2 + 21 xx 7 + (7)^2]`
`=20020`
`=20.02 `litres
The slant height of the bucket
\[l = \sqrt{h^2 + \left( r_1 - r_2 \right)^2}\]
\[ = \sqrt{900 + \left( 21 - 7 \right)^2}\]
\[ = \sqrt{900 + 196}\]
\[ = \sqrt{1096} = 33 . 105 cm\]
Total C.S.A. of the bucket
\[= \pi\left( r_1 + r_2 \right) \times l\]
\[ = \pi\left( 21 + 7 \right) \times 33 . 1\]
\[= 88 \times 33 . 1\]
\[ \approx 2913 {cm}^2\]
Area of the base
`=pir^2`
`=22/7 xx 7^2`
`=154`
Total sheet required to make this bucket
\[= 2913 + 154\]
\[ = 3067 {cm}^2\]
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