Question

Question 7
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.

Answer 1

Radius of cylinder = 18 cm, height = 32 cm
Height of cone = 24 cm
Volume of cylinder
$=\pi r^{2}h$
$=\pi \times {18}^2\times 32$
Volume of cone = Volume of cylinder
Volume of cone
$=\frac{1}{3}\pi r^2\times 24$
Hence, radius of cone can be calculated as follows:
$r^2=\frac{3\times \pi \times {18}^2\times 32}{\pi \times 24}$
$Or{r}^2={18}^2\times 2^2$
$Or,r=36cm$
Now, slant height of conical heap can be calculated as follows:
$l=\sqrt{h^2+r^2}$
$=\sqrt{{24}^2+{36}^2}$
$=\sqrt{576+1296}$
$=\sqrt{1872}=12\sqrt{13}cm$