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

Options

• 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, `"R" = 44/2    "cm"=24/2  "cm", "h" = 35   "cm"`

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

`= 1/3 pi"h"["R"^2 + "r"^2+"Rr"] "cm"^3`

`= 1/3 xx 22/7xx35xx[(22)^2 + (12)^2 +(22xx12)] "cm"^3`

`= (110/3 xx 892) "cm"^2`

`= ((110xx892)/(3xx1000))` litres

= 32.7 litres

Hence, the capacity of the bucket is 32.7 litres.