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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
Solution
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.
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