Q16 of 56 Page 13

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.

Use π = 22/7. (CBSE 2011)

Given: Height of the frustum = h = 21 cm


Radius of lower end of the frustum = r = 10 cm


Radius of upper end of the frustum = R = 20 cm


Now, volume of the frustum = (1/3) × π [R2 + r2 + Rr] × h


= (1/3) × (22/7) × [400 + 100 + 200] × 21


= 700 × 22


15400 cm3


Now, volume of frustum in liters = 15400/1000 = 15.4 lts.


(∵ 1000cm3 = 1 lt)


Now, cost of milk at ₹ 30 per liter = 15.4 × ₹ 30


= ₹ 462

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