Question

A milk container of height 16 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 cm and 20 cm respectively . Find the cost of milk at the rate of ₹44 per litre which the container can hold.

Answer 1

Radius, r₁ = 8 cm and r₂ = 20 cm
Height, h = 16 cm
Volume of milk that the container can hold
$$\begin{gathered} V=\frac{1}{3}\mathrm{\pi h}\left({\mathrm{r}}_1^2+{\mathrm{r}}_1{\mathrm{r}}_2+{\mathrm{r}}_2^2\right) \\ \mathrm{V}=\frac{1}{3}\mathrm{\pi }\times 16\left(8^2+8\times 20+{20}^2\right) \\ \mathrm{V}=10459.42{\mathrm{cm}}^3=10.45942\mathrm{liters} \end{gathered}$$
Cost of milk will be $10.45942\times 44=Rs460.21$