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A milk container of height $16cm$ is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as $8cm$ and $20cm$ respectively. Find the cost of milk at the rate of $Rs.44$ per liter which the container can hold.
A milk container of height $16cm$ is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as $8cm$ and $20cm$ respectively. Find the cost of milk at the rate of $Rs.44$ per liter which the container can hold.
CBSE | Class 10 | Exercise 16.3 | Maths | RD Sharma | Surface Areas And Volumes
A milk container of height $16cm$ is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as $8cm$ and $20cm$ respectively. Find the cost of milk at the rate of $Rs.44$ per liter which the container can hold.

As per the given information,

A milk container in a form of frustum of a cone with,

Radius of the lower end $\left( {{r}_{1}} \right)=8cm$

And radius of the upper end $\left( {{r}_{2}} \right)=20cm$

Let us assume h be its height of container, $h=16cm$

Therfore, according to the question the capacity of the container $=$ Volume of frustum of the cone

$=1/3\pi \left( r_{2}^{2}+r_{1}^{2}+{{r}_{1}}{{r}_{2}} \right)h$

$=1/3\pi \left( {{20}^{2}}+{{8}^{2}}+\left( 20 \right)\left( 8 \right) \right)\times 16$

$=10459.42c{{m}^{3}}$

$=10.46litres$

Now, given that cost of 1 litre of milk in the question $=Rs44$

Hence, the cost of $10.46$ litres of milk $=$ Rs $\left( 44\times 10.46 \right)=Rs.460.24$

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