The Diameters of Two Cones Are Equal. If Their Slant Heights Are in the Ratio 5 : 4, the Ratio of Their Curved Surface Areas, is - Mathematics

MCQ

The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, the ratio of their curved surface areas, is

•  4 : 5

• 25 : 16

•  16 : 25

• 5 : 4

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 = πrl

Now there are two cones with base radius and slant heights as r_1 ,l_1 & r_2 , l_2 respectively.

The ratio between slant heights of the two cones is given as 5 : 4, we shall use them by introducing a constant ‘k’

So, now   l_1= 5k

l_2 = 4k

Since the base diameters of both the cones are equal we get that r_1 = r_2 = r

Using these values we shall evaluate the ratio between the curved surface areas of the two cones

(C.S.A_1)/(C.S.A_2) = (pir_1l_1)/(pi r_2l_2)

=(pir(5k))/(pir(4k)

=5/4

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 11 | Page 25