The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm . The capacity of the bucket is

Options

A. `32.7 L`
B. `33.7 L`
C. `34.7L`
D. `31.7L`

Answer

A

Explanation

Given , dimeter of one end of the bucket,
`2R = 44 rArr R = 22 cm " "[therefore "diameter", r = 2 xx "radius "]`
and diameter of the other end,
`2r = 24 rArr r = 12 cm " "[therefore "diameter", r = 2 xx "radius "]`
Height of the bucket , h = 35cm
Since, the shape of bucket is look like as frustum of a cone.
`therefore` Capacity of the bucket = Volume of the frustum of the cone
`= (1)/(3) pi h [h^(2) + r^(2) +Rr]`
`= (1)/(3) xx pi xx 35 [(22)^(2) + (12)^(2) + 22 xx 12]`
`= (35pi)/(3) [484 + 144 + 264]`
`(35 pi xx 892)/(3) = (35 xx 22 xx 892)/(3 xx7)`
`= 32706.6 cm^(3) = 32.7 L " "[therefore 1000 cm^(3) = 1L]`
Hence, the capacity of bucket is 32.7 L