Question

If the height &the radius of a cone are tripled then find the ratio of volume of new cone and of that of original cone.

Answer 1

relation between volume Nd radius Nd height getting from formula

Answer 2

Answer:

27:1

Step-by-step explanation:

Let the height of original cone be h

Let  the radius of original cone be r

Volume of original cone = $\frac{1}{3} \pi r^2 h$

We are given that the height & the radius of a cone are tripled .

So, new radius = 3r

New height = 3h

Volume of new cone = $\frac{1}{3} \pi (3r)^2 \times 3h$

The ratio of volume of new cone and of that of original cone:

$\frac{\frac{1}{3} \pi (3r)^2 \times 3h}{\frac{1}{3} \pi r^2 h}$

$\frac{ 9r^2 \times 3h}{ r^2 h}$

$\frac{ 27}{1}$

Hence The ratio of volume of new cone and of that of original cone is 27:1