Question

The ratio of the radii of two cones is 2: 3 and the ratio of their slant heights is 9 : 4. Then the ratio of their curved surface areas is _______(a) 3 : 2
(b) 1:2
(c) 1: 3
(d) 2 :3

Answer 1

Answer:

option

Step-by-step explanation:

b................

is crt

Answer 2

Answer:

Option (a),3:2 is correct

Step-by-step explanation:

Curved surface area of cone:

$\boxed{CSA = \pi \: r \: l }$

Let the radius of cone1 is r1 and that of cone 2 is r2 and the slant height of cone 1 is l1 and that of cone 2 is l2

So, according to the question

$\frac{r_1}{r_2} = \frac{2}{3} \\ \\ \frac{l_1}{l_2} = \frac{9}{4}$

Ratio of CSA of both the cone:

$\frac{CSA_1}{CSA_2} = \frac{\pi \times \: r_1 \times \: l_1}{\pi \times \: r_2 \times \: l_2} \\ \\ \frac{CSA_1}{CSA_2} = \frac{r_1 \times \: l_1}{r_2 \times \: l_2} \\ \\ \frac{CSA_1}{CSA_2} = \frac{r_1}{r_2} \times \frac{l_1}{l_2} \\ \\\frac{CSA_1}{CSA_2} = \frac{2}{3} \times \frac{9}{4} \\ \\ \frac{CSA_1}{CSA_2} = \frac{3}{2}$

Hope it helps you.