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A milk container of height $16 cm$ is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as $8 cm$ and $20 cm$ , respectively. What is the cost of milk at the rate of Rs.22 per litre, which the container can hold?

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Rs.230.10

Rs.200.10

Rs.230

Rs.240

answer is A.

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Detailed Solution

Given that height (h) is 16cm, radius of lower end (r) is 8cm and upper end (R) is 20cm.
We have the following formula,
Volume of frustum

= π h 3 R 2 + r 2 + R r cm 3

The Volume of frustum will be,

= π (16) 3 (20) 2 + 82 + (20) (8) cm 3 = 22 (16) 21 400 + 64 + 160 cm 3 = 10459.428 c m 3

Volume of frustum is

10.459 l i t r e s

. (1litre=1000

c m 3

)
Cost of milk the container can hold will be,
The cost of milk per litre = Rs.22
10.459 litres of milk will cost,

= 22 × 10.459 = 230.10

Thus, the container holds the milk that costs Rs.230.10.
Therefore the correct option is 1.

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