Question

A milk container is in the form of frustum of a cone of height 18 cm with radii of its upper and lower ends being 8 cm and 32 cm, respectively. Find the amount of milk that can be used to completely fill the container and the cost of doing so at the rate of Rs 20 per litre.

Answer 1

Greater radius of the frustum = R = 32 cm
Smaller radius of the frustum = r = 8 cm
Height of the frustum = h = 18 cm

Capacity of the frustum
$$\begin{gathered} =\frac{1}{3}\mathrm{\pi }h\left(R^2+r^2+Rr\right) \\ =\frac{1}{3}\times \mathrm{\pi }\times 18\left({32}^2+8^2+32\times 8\right) \\ =\frac{22}{7}\times 6\times 1344 \\ =25344{\mathrm{cm}}^3=25.344\mathrm{litres} \end{gathered}$$

Cost of 1 l is Rs 20.
So, total cost of filling the container with milk$=25.344\times 20=\mathrm{Rs}506.88$