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

Options

•  2 : 1

• 4 : 1

• 8 : 1

• 1 : 1

Answer 1

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`