The diameters of the two circular ends

Question:

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

(a) 32.7 L                     

(b) 33.7 L           

(c) 34.7 L                

(d) 31.7 L

Solution:

(a) Given, diameter of one end of the bucket

$2 R=44 \Rightarrow R=22 \mathrm{~cm}$ $[\because$ diameter, $r=2 \times$ radius $]$

and diameter of the other end,

$2 r=24 \Rightarrow r=12 \mathrm{~cm} \quad[\because$ diameter, $r=2 \times$ radius $]$

Height of the bucket, $h=35 \mathrm{~cm}$

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

$=\frac{1}{3} \pi h\left[R^{2}+r^{2}+R r\right]$

$=\frac{1}{3} \times \pi \times 35\left[(22)^{2}+(12)^{2}+22 \times 12\right]$

$=\frac{35 \pi}{3}[484+144+264]$

$=\frac{35 \pi \times 892}{3}=\frac{35 \times 22 \times 892}{3 \times 7}$

$=32706.6 \mathrm{~cm}^{3}=32.7 \mathrm{~L} \quad\left[\because 1000 \mathrm{~cm}^{3}=1 \mathrm{~L}\right]$

Hence, the capacity of bucket is 32.7 L.

 

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