Question

A cylindrical bucket of height 10 cm and radius 5 cm is overturned to form a conical heap of sand of radius 5 cm. Find the height of the cone.

• A. 40 cm
• B. 10 cm
• C. 30 cm
• D. 20 cm

Answer 1

The correct option is C 30 cm

Given, the cylindrical bucket is overturned to form a conical heap of sand.

So, volume of the cylinder = volume of cone formed

$\text{Volume of cylinder}=\pi r^{2}h=\frac{22}{7}\times 5^2\times 10=\frac{5500}{7}c{m}^2$

$\text{Volume of cone}=\frac{1}{3}\pi r^{2}h$

$\because$ Volume of cylinder = Volume of cone

$\Rightarrow \frac{5500}{7}=\frac{1}{3}\pi r^{2}h$
$\Rightarrow \frac{5500}{7}=\frac{1}{3}\times \frac{22}{7}\times 5^2\times h$
$\Rightarrow h=30cm$
Therefore, the height of the cone is 30 cm.