Question

The bottom of a right cylindrical shaped vessel made from metallic sheet is closed by a cone shaped vessel as shown in the figure. The radius of the circular base of the cylinder and radius of the circular base of the cone are each equal to 7 cm. If the height of the cylinder is 20 cm and height of cone is 3 cm, calculate the cost of milk to completely fill this vessel at the rate of Rs. 20 per litre.

Answer 1

Given that,

The radius of both cylindrical vessel and cone is $7cm$.

The height of the cylindrical vessel is $20cm$ and that of the cone is $3cm$.

The cost of one litre milk is $Rs.20$.

To find out,

The cost of filling the vessel completely with milk.

We know that,

Volume of cylinder = $\pi r^{2}h$

$\Rightarrow \frac{22}{7}\times 7\times 7\times 20$

$\Rightarrow 3080{cm}^3$

We also know that,

Volume of Cone $=\frac{1}{3}\pi r^{2}h$

$\Rightarrow \frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 3$

$\Rightarrow 154{cm}^3$

Now,

Total volume of cylindrical vessel = volume of cylinder - volume of cone

$\Rightarrow 3080-154=2926{cm}^3$

$\therefore$ total milk required to completely fill the vessel $=2.926l$ $[1l=1000c{m}^3]$

$\therefore$The cost of filling milk $=2.926\times 20=Rs.58.520$

Hence, the cost of milk required to completely fill the vessel is $Rs.58.520$