# 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 - Mathematics

MCQ

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

•  2 : 1

• 4 : 1

• 8 : 1

• 1 : 1

#### Solution

The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as

Curved Surface Area = pirl

Now there are two cones with base radius, slant height and Curved Surface Area (C.S.A) as r_1,l_1, C.S.A_1 & r_2, l_2,c,S,A_2 respectively.

It is given that C.S.A_1  = 2(c,S,A_2 ) and also that l_2 = 2(l_1). Or this can also be written as

(l_2)/(l_1)=2

(C.S.A_1) / (C.S.A_2) = (pir_1l_1)/(pir^2l^2)

2(C.S.A_2) / (C.S.A_2) = (pir_1l_1)/(pir^2l^2)

r_1/r_2=(2l_2)/l_1

r_1/r_2=((2)(2))/1

r_1/r_2=4/1

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 20 Surface Areas and Volume of A Right Circular Cone
Q 7 | Page 24