Question

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

विकल्प

• 31.7 liters

• 32.7 liters

• 33.7 litres

• 34.7 litres

Answer 1

32.7 litres

Let R and r be the radii of the top and base of the bucket, respectively and let h be its height. 

Then, ${\displaystyle \text{R}=\frac{44}{2} \text{cm}=\frac{24}{2} \text{cm},\text{h}=35 \text{cm}}$

Capacity of the bucket = Volume of the frustum of the cone

${\displaystyle =\frac{1}{3}\pi \text{h}[{\text{R}}^2+{\text{r}}^2+\text{Rr}]{\text{cm}}^3}$

${\displaystyle =\frac{1}{3}\times \frac{22}{7}\times 35\times [{\left(22\right)}^2+{\left(12\right)}^2+(22\times 12)]{\text{cm}}^3}$

${\displaystyle =(\frac{110}{3}\times 892){\text{cm}}^2}$

${\displaystyle =\left(\frac{110\times 892}{3\times 1000}\right)}$ litres

= 32.7 litres

Hence, the capacity of the bucket is 32.7 litres.