Question

A container is in the form of frustum of a cone of height 35 cm with radii of its lower and upper ends as 18cm and 24cm respectively. Find the cost of milk which can fill the container at the rate of Rs 32/liter

Answer 1

Given :-

• height of frustum = 35cm
• r1 = 18cm
• r2 = 24cm

To find :-

• cost of milk which can fill the container at the rate of Rs. 32/L

Solution :-

$volume \: of \: frustum \: = \frac{1}{3} \pi \: h( {r1}^{2} + {r2}^{2} + r1r2) \\ - - - - - - - - - - - \\ = > \underline{substituting \: values \: in \: the \: formula} \\ = > volume = \frac{1}{3} \times \frac{22}{7} \: \times 35( {18}^{2} + {24}^{2} + 18(24)) \\ = > \frac{1}{3} \times 22 \times 5(324 + 576 + 432) \\ = > \frac{1}{3} \times 22 \times 5 \times 1332 \\ \underline{(cancel \: (3) \: with \: (1332) }\: \\ = > 22 \times 5 \times 444 \: \\ = > 48840 \\ = > volume \: = 48840 {cm}^{3}$

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converting cm^3 to litres :-

1 litre = 1000 cm^3

= 48840/1000

= 48.84 litres.

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cost of filling the container for 1 litre is

= Rs 32

cost of filling the container for 48.84 litres

= 32 x 48.84

= 1,562.8 Rs.