Question

A cylindrical bucket, 32 cm high and with radius of base 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. [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

Height of cylindrical bucket = h =32 cm

Radius of cylindrical bucket = r = 18 cm

Height of conical heap $=h_1=24cm$

Let slant height of conical heap =$lcm$

Let radius of cylindrical heap $=r_{1}cm$

According to given condition we have

Volume of cylindrical bucket = Volume of conical heap

$\Rightarrow \pi .r^2.h=\frac{1}{3}\times \pi \left(r_1{)}^2\right(h_1)$

$\Rightarrow 3\times 18\times 18\times 32=(r_1{)}^2\times 24$

$\Rightarrow (r_1{)}^2=1296$

$\Rightarrow r_1=\sqrt{1296}=36cm$

$l=\sqrt{(r_1{)}^2+(h_1{)}^2}=\sqrt{(36{)}^2+(24{)}^2}=\sqrt{1872}$

$\Rightarrow l=12\sqrt{13}cm$