Question

Question 18
The diameters of the two circles ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is
(A) 32.7 litres
(B) 33.7 litres
(C) 34.7 litres
(D) 31.7 litres

Answer 1

Option (B) is correct.
Given , diameter of one end of the bucket,
$2R=44\Rightarrow R=22cm$ $[\because diameter,d=2\times radius]$
And diameter of the other end.
$2r=24\Rightarrow r=12cm$ $[\because diameter,d=2\times radius]$
Height of the bucket , h = 35 cm
Since, the shape of bucket is look like as frustum of cone.
$\therefore$ Capacity of the bucket = Volume of the frustum of the cone
$=\frac{1}{3}\pi h[R^2+r^2+Rr]=\frac{1}{3}\times \pi \times 35\left[\right(22{)}^2+(12{)}^2+22\times 12]=\frac{35\pi }{3}[484+144+264]=\frac{35\pi \times 892}{3}=\frac{35\times 22\times 892}{3\times 7}=32706.6c{m}^3\left(approx\right)=32.7L[\because 1000c{m}^3=1L]$