A bucket, made of metal sheet, is in the form of a cone whose height is 35 cm and radii of circular ends are 30 cm and 12 cm. How many litres of milk it contains if it is full to the brim? If the milk is sold at Rs 40 per litre, find the amount received by the person.

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Solution

The given bucket is in the form of the frustum of a cone.
Height, h = 35 cm
r₁ = 30 cm
r₂ = 12 cm
$Volume = \frac{π}{3} h ({r_{1}}^{2} + {r_{2}}^{2} + r_{1} r_{2}) = \frac{π}{3} \times 35 (30^{2} + 12^{2} + 30 \times 12) = \frac{π}{3} \times 35 (900 + 144 + 360) = \frac{π}{3} \times 35 \times (1404) = 51433.2 {cm}^{3}$
= 51.4 litres
Selling price of the milk = Rs 40/litre
So, selling price of 51.4 litres of milk will be $51.4 \times 40 = Rs 2056$

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