Question

Choose the correct answer in each of the following :

A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to make n solid cones of height 1cm and base radius 1mm. The value of n is

(a) 450 (b) 1350 (c) 4500 (d) 13500

Answer 1

Ans-d

Radius of cylinder =3cm
height h =5cm
height of the cone H =1cm
radius R =1mm=$\frac{1}{10}=0.1cm$
since the cylinder is recast into the cone, then
let n be the number of cones that can be formed from the cylinder
n x (volume of the cone) = (volume of cylinder)
$n\times \frac{1}{3}\pi R^{2}H=\pi r^{2}h$
$n\times 0.1\times 0.1\times \frac{1}{3}=3\times 3\times 5$
$0.01n=45\times 3$
$n=\frac{135}{0.01}$
$n=13500$
hence 13500 number of cones can be formed from the cylinder.