Question

Two right circular cones of equal curved surface area have slant height is ratio of 3:5 find the ratio of their radii

Answer 1

Answer:

cones:

A= πrl, r=A/πI

Ratio .:

Lsa=l:l

slant height=I. 3:5

I/πx3: I/πx5

= 1/3:1/5

=5:3. ratio of radii. Ans

Answer 2

Given,

The curved surface area of the two cones is equal.

The ratio of their slant height = 3:5

To find,

The ratio of their radii.

Solution,

The ratio of their radii is 5:3.

We can easily solve this problem by following the given steps.

We know that the formula for the curved surface area of a cone is πrl where r is its radius and l is the slant height.

Let's take the radius and slant height of the first cone to be R and L and that of the second cone to be r and l.

The ratio of their slant height = 3:5

L:l = 3:5

Let's take L to be 3x units and l to be 5x units.

According to the question,

The curved surface area of the two cones is equal.

πRL = πrl

RL = rl

R/r = l/L

R/r = 5x/3x (Putting the value of L and l)

R/r = 5/3

Hence, the ratio of their radii is 5:3.