Question

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.

Answer 1

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

\[= 2913 + 154\]

\[ = 3067 {cm}^2\]