Question

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm³ of water. The radii of the top and bottom circular ends are
20 cm and 12 cm, respectively. Find the height of the bucket. [Use $\mathrm{\pi }$ = 3.14] [CBSE 2006C]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{upper}\mathrm{end},R=20\mathrm{cm}\mathrm{and} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{lower}\mathrm{end},r=12\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{bucket}\mathrm{be}h. \\ \mathrm{As}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{bucket}=12308.8{\mathrm{cm}}^3 \\ \Rightarrow \frac{1}{3}\mathrm{\pi }h\left(R^2+r^2+Rr\right)=12308.8 \\ \Rightarrow \frac{1}{3}\times 3.14\times h\times \left({20}^2+{12}^2+20\times 12\right)=12308.8 \\ \Rightarrow \frac{3.14h}{3}\times \left(400+144+240\right)=12308.8 \\ \Rightarrow \frac{3.14h}{3}\times 784=12308.8 \\ \Rightarrow h=\frac{12308.8\times 3}{3.14\times 784} \\ \therefore h=15\mathrm{cm} \end{gathered}$$

So, the height of the bucket is 15 cm.