Question

a) What is the volume of a solid metal cylinder of height 4 centimetres and radius 5 centimetres?
b) This solid is melted and recast in to 5 cones of equal height and radius 2 centimetres. Find the height of such a cone.

Answer 1

(a) Height of cylinder, $h=4cm$
Radius of cylinder, $r=5cm$
Volume of cylinder $=\pi r^{2}h$
$=3.14\times 5^2\times 4{cm}^3$
$=314{cm}^3$
(b) Radius of re-casted cone, $r=2cm$
Let, height of re-casted cone $=h$
Volume of each cone $=\frac{314}{5}{cm}^3=62.8{cm}^3$
Volume of cone $=\frac{1}{3}\pi r^{2}h$

$62.8=\frac{1}{3}\times 3.14\times (2{)}^2\times h$

$h=\frac{62.8\times 3}{4\times 3.14}cm$
$h=15cm$
Height of the cone is $15cm$.