A milk container of height $ 16 \mathrm{~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 \mathrm{~cm} $ and $ 20 \mathrm{~cm} $ respectively. Find the cost of milk at the rate of $ ₹ 44 $ per litre which the container can hold.
Given:
A milk container of height \( 16 \mathrm{~cm} \) is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as \( 8 \mathrm{~cm} \) and \( 20 \mathrm{~cm} \) respectively.
To do:
We have to find the cost of milk at the rate of \( ₹ 44 \) per litre which the container can hold.
Solution:
Height of the milk container $h = 16\ cm$
Radius of the lower end of the milk container $r_1 = 8\ cm$
Radius of the upper end of the milk container $r_2 = 20\ cm$
Therefore,
Volume of the milk container $=\frac{\pi}{3}[r_1^2+r_2^2+r_1r_2]\times h$
$=\frac{22}{3\times7}(8^2+20^2+8\times20)\times16$
$=\frac{22 \times 16 \times 624}{21}$
$=\frac{219648}{21}$
$=10459.42 \mathrm{~cm}^{3}$
$=10.45942 \mathrm{~L}$
The volume of the milk container is $10459.42 \mathrm{~cm}^{3}$
Cost of $1 \mathrm{~L}$ of milk $=Rs.\ 44$
Cost of $10.45942 \mathrm{~L}$ of milk $=Rs.\ 44 \times 10.45942$
$=Rs.\ 460.24$
The cost of the milk is $Rs.\ 460.24$.
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