Question

A girl fills a cylindrical bucket $32cm$ in height and $18cm$ in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is $24cm$, find its radius.

• A. $26cm$
• B. $34cm$
• C. $28cm$
• D. $36cm$

Answer 1

The correct option is D $36cm$

Height of conical heap, $h=24cm$.

Let the radius of the conical heap be $r$ cm.

Then, volume of conical heap

$=\frac{1}{3}\pi r^{2}h=(\frac{1}{3}\times \frac{22}{7}\times r^2\times 24)$.

Volume of sand = Volume of cyledrical bucket = $\pi r^{2}h=(\frac{22}{7}\times 18\times 18\times 32)$

Now, Volume of conical heap = Volume of sand

$\Rightarrow (\frac{1}{3}\times \frac{22}{7}\times r^2\times 24)=(\frac{22}{7}\times 18\times 18\times 32)$

$r=\sqrt{(18\times 18\times 4)}=(18\times 2)cm=36cm$

$\therefore$ Radius of the heap $=36cm$