Question

A cylindrical bucket of diameter 28 cm and height 20 cm was full of sand. When the sand in the bucket was poured on the ground, the sand got converted into a shape of a cone. If the height of the cone was 14 cm, what was the base area of the cone ?

Answer 1

Radius of the bucket, r = $\frac{28}{2}$ = 14 cm

Height of the bucket, h = 20 cm

Height of the cone, H = 14 cm

Let the radius of the base of the cone be R cm.

∴ Area of the base of the cone = $\mathrm{\pi }$R²

Now,

Volume of sand in the cone = Volume of sand in the cylindrical bucket

$$\begin{gathered} \therefore \frac{1}{3}\mathrm{\pi }{R}^{2}H=\mathrm{\pi }{r}^{2}h \\ \Rightarrow \mathrm{\pi }{R}^2=\frac{3\mathrm{\pi }{r}^{2}h}{H} \\ \Rightarrow \mathrm{\pi }{R}^2=\frac{3\times {\displaystyle \frac{22}{7}}\times {\left(14\right)}^2\times 20}{14} \\ \Rightarrow \mathrm{\pi }{R}^2=2640{\mathrm{cm}}^2 \end{gathered}$$
Thus, the base area of the cone is 2640 cm².