#### A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

r = 36 cm, $l = 12\sqrt{13} cm$

Height of cylindrical bucket (h1) = 32 cm

Volume = $\pi r{_{1}}^{2}h_{1}$

$=\frac{22}{7}\times 18 \times 18 \times 32$

Height of conical heap (h2) = 24 cm

Volume  $=\frac{1}{3}\pi r_{2}^{2}h_{2}=\frac{1}{3}\times \frac{22}{7} \times r_{2}^{2}\times 24$

According to question

Volume of cylindrical bucket = Volume of conical heap

$\frac{22}{7}\times 18 \times 18 \times 32 = \frac{1}{3}\times \frac{22}{7}\times r_{2}^{2}\times 24$

$=\frac{18 \times 18 \times 32 \times 3}{24}=r_{2}^{2}$

$=18^{2}\times 4 = r_{2}^{2}$

$r_{2}=\sqrt{18 \times 18 \times 2 \times 2}$

$r_{2}= 18 \times 2 = 36\; cm$

Slant height $(l)=\sqrt{r_{2}^{2}+h_{2}^{2}}$

$\sqrt{36^{2}+24^{2}}$

$=\sqrt{1296+576}$

$=\sqrt{1872}$

$\sqrt{12 \times 12 \times 13}$

$l=12\sqrt{13}cm$