Question

The ratio of the radii of two right circular cones of same height is 1:3. Find the ratio of their curved surface area when the height of each cone is 3 times the radius of the smaller cone.

Answer 1

hope it's clear........

Answer 2

The ratio of  their curved surface area is √5:9

Step-by-step explanation:

We are given that The ratio of the radii of two right circular cones of same height is 1:3.

Let the ratio be x

So, radius of small cone = x

Radius of large cone = 3x

Height of both the cones are same .

We are given that the height of each cone is 3 times the radius of the smaller cone

So, Height = 3x

Curved surface area of cone = $\pi r \sqrt{h^2+r^2}$

So, ratio of their curved surface area = $\frac{\pi \times x \times \sqrt{(3x)^2+x^2}}{\pi \times 3x \times \sqrt{(3x)^2+(3x)^2}}$

                                                             =$\frac{\sqrt{10x^2}}{3 \times \sqrt{18x^2}}$

                                                             =$\frac{\sqrt{10}x}{3 \sqrt{18}x}$

                                                             =$\frac{\sqrt{5}\sqrt{2}}{9 \sqrt{2}}$

                                                             =$\frac{\sqrt{5}}{9}$

Hence The ratio of  their curved surface area is √5:9

#Learn more :

Two right circular cones of equal curved surface areas have slant heights in the ratio of 3:5.

Find the ratio of their radii?​

https://brainly.in/question/14231747