Question

The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is
A. 2 : 1
B. 4 : 1
C. 8 : 1
D. 1 : 1

Answer 1

The ratio of the radii of two cones is 2 : 1. Hence, option (A) is correct.

• The formula for the curved surface area of a cone is given as :

C.S.A. = π × radius × slant height

• Let the radius of one cone be r, and its slant height be l.

According to the given condition,

Slant height of the other cone = 2l

Let the radius of the other cone be r'

• From the formula,

C.S.A of the first cone = πrl

C.S.A. of the second cone = π.r'.2l = 2πr'l

• According to the question,

C.S.A. of the first cone = 2 × C.S.A. of the second cone

Or, πrl = 2πr'l  -(i)

• The ratio of the radii of two cones = r / r'

Therefore, from equation (i),

r / r' = 2πl / πl

Or, r / r' = 2 / 1

Or, r : r' = 2 : 1

• Therefore, the ratio of the radius of first cone to the radius of second cone = 2 : 1