Question

A bucket of height 24 cm is in the form of frustum of a cone whose circular ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of ₹30 per litre, which the bucket can hold. [CBSE 2013C]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{frustum},h=24\mathrm{cm}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{open}\mathrm{end},R=\frac{42}{2}=21\mathrm{cm}\mathrm{and} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{close}\mathrm{end},r=\frac{28}{2}=14\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{bucket}=\frac{1}{3}\mathrm{\pi }h\left(R^2+r^2+Rr\right) \\ =\frac{1}{3}\times \frac{22}{7}\times 24\times \left({21}^2+{14}^2+21\times 14\right) \\ =\frac{176}{7}\times \left(441+196+294\right) \\ =\frac{176}{7}\times 931 \\ =23408{\mathrm{cm}}^3 \\ =23.408\mathrm{L}\left(\mathrm{As},1000{\mathrm{cm}}^3=1\mathrm{L}\right) \\ \therefore \mathrm{The}\mathrm{cost}\mathrm{of}\mathrm{the}\mathrm{milk}=30\times 23.408=₹702.24 \end{gathered}$$

So, the cost of the milk which the bucket can hold is ₹702.24.