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Question
An open metal bucket is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at Rs. 30 per litre. `[User pi22/7]`
Solution
Height of frustum of cone, h = 21 cm
Radius of lower end, r = 10 cm
Radius of upper end, R = 20 cm
Volume of frustum of cone `=1/3 pir (R^2+r^2+Rr)`
Volume of milk required to completely fill the bucket
`=1/3xx22/7xx21cmxx[(20 cm)^2+(10cm)^2+20cmxx10 cm]cm^3`
`=22xx(400+100+200)cm^2`
`=22xx700cm^2`
`=15400 cm^2`
`=15400/1000 litre` (∵ 1000 cm3= 1 litre)
`=15.4 litre`
Cost of milk = Rs 30 per litre
Thus, cost of milk that can completely fill the bucket = Rs (30 × 15.4) = Rs 462
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