Question

if the radius of base and the volume of right circular cone are doubled what is the ratio of the length of the larger cone to that of the smaller cone?

Answer 1

Given:
radius of smaller cone=r
height = h1
volume of cone=V=1/3(πr^2h)----(1)

second cone(larger)
radius=2r
height=h2
volume=-2/3(πr^2h2)----(2)

1/3(πr^2h1)=2/3(πr^2h2)
h1/3=(2/3 )h2
h2/h1 =1/2
Therefore ratio of
length of the larger cone to that of the smaller cone is 1: 2

Answer 2

Answer:

The ratio is 2 : 1.

Step-by-step explanation:

Let r be the radius of the cone and h be the length or height of the cone,

Then, volume of the cone,

$V=\frac{1}{3}\pi (r)^2 h-------(1)$

According to the question,

After enlarging this cone,

New radius is 2r and new volume is 2V

Let H be the length of larger cone,

Then,

$2V = \frac{1}{3}\pi (2r)^2 H= \frac{1}{3}\pi(4r^2)H-------(2)$

Equation (2) / Equation (1),

We get,

$2=\frac{4H}{h}$

$\implies \frac{H}{h}=\frac{2}{1}$

Hence, the ratio of the length of the larger cone to that of the smaller cone is 2 : 1.