Question

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.

Answer 1

As we know if a solid object turn into another or if a thing which take a shape of one object turn into another object then there volume will be equal.
Volume of cylinder = Volume of cone

$\pi$ ×$R^2$×H= $\frac{1}{3}$ × $\pi$×$r^2$× h

$\Rightarrow$ 18 × 18 × 32 = $\frac{1}{3}$ × $r^2$ × 24

$\Rightarrow$ 18 × 18 × 32 = 8 × $r^2$

$\Rightarrow$ 18 × 18 × 4 = $r^2$

$\Rightarrow$ r = $\sqrt{18\times 18\times 4}$

r = 36
h= 24 cm
Slant height = $\sqrt{{36}^2+{24}^2}$
Slant height = $\sqrt{1872}$
Slant height=12√13 cm
Slant height = 12√13 cm