Question

A cylindrical bucket of diameter 28 cm and a height of 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 =  \[\pi\]R²

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

\[\therefore \frac{1}{3}\pi R^2 H = \pi r^2 h\]
\[ \Rightarrow \pi R^2 = \frac{3\pi r^2 h}{H}\]
\[ \Rightarrow \pi R^2 = \frac{3 \times \frac{22}{7} \times \left( 14 \right)^2 \times 20}{14}\]
\[ \Rightarrow \pi R^2 = 2640 {cm}^2\]

Thus, the base area of the cone is 2640 cm².