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 slant height

• A. $13\sqrt{12}$
• B. $12$
• C. $12\sqrt{13}$
• D. $13$

Answer 1

Answer: (C)

$12\sqrt{13}$

Height of cylindrical bucket, H = 32 cm.

Radius of cylindrical bucket, R = 18 cm.

Volume of sand

=$\pi R^{2}H=(\frac{22}{7}\times 18\times 18\times 32)c{m}^3$

Slant Height

$l=\sqrt{h^2+r^2}=\sqrt{(24{)}^3+(36{)}^2}=\sqrt{1872}=12\sqrt{13}cm$