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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 ______.
Options
32.7 litres
33.7 litres
34.7 litres
31.7 litres
Solution
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 31.7 litres.
Explanation:
Given, diameter of one end of the bucket
2R = 44
⇒ R = 22 cm ...[∵ Diameter, r = 2 × radius]
And diameter of the other end,
2r = 24
⇒ r = 12 cm ...[∵ Diameter, r = 2 × radius]
Height of the bucket,
h = 35 cm
Since, the shape of bucket is look like as frustum of a cone.
∴ Capacity of the bucket
= Volume of the frustum of the cone
= `1/3 pi"h"["R"^2 + "r"^2 + "Rr"]`
= `1/3 xx [pi xx 35(22)^2 + (12)^2 + 22 xx 12]`
= `(35pi)/3 [484 + 144 + 264]`
= `(35pi xx 892)/3`
= `(35 xx 22 xx 892)/(3 xx 7)`
= 32706.6 cm3
= 32.7 litres ...[∵ 1000 cm3 = 1 litre]
Hence, the capacity of bucket is 32.7 litres.
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