Question

A 32cm tall cylindrical bucket of base diameter 36cm, is filled with sand and this container is emptied on the ground forming a conical heap of sand. If the height of the heap is 24cm. Find the slant height of the heap.

• A. 12$\sqrt{13}$
• B. 15$\sqrt{13}$
• C. 13$\sqrt{13}$
• D. 12$\sqrt{15}$

Answer 1

The correct option is A

12$\sqrt{13}$

Volume of the cylinder = $\pi r^{\prime 2}h=\pi \times (18{)}^2\times 32=10368\pi c{m}^3$

Volume of the cone = $\frac{1}{3}\pi r^{\prime 2}h=\frac{1}{3}\pi \times (r{)}^2\times 24=8\pi (r{)}^{2}c{m}^3$

Volume of cylinder = Volume of cone

10368 $\pi$ = 8$\pi (r{)}^2$

$(r{)}^2$ = 1296

r = 36cm

Slant height of cone (l) = $\sqrt{(r{)}^2+(h{)}^2}$

$l=\sqrt{(36{)}^2+(24{)}^2}$

l = 12$\sqrt{13}$