Question

If the ratio of radii of two spheres is 2: 5, then the ratio of their curved surfaces areas is_______
(a) 8 : 125
(b) 4: 25
(c) 25 : 4
(d)125:8

Answer 1

Answer:

(b) 4:25

Step-by-step explanation:

Curved surface area of sphere (A) =4*pi*r^2

hence area is directly proportional to r^2.

R1:R2 = 2:5 (given)

Therefore ratio of their area

A1:A2 = (2:5)^2

= 4:25

Answer 2

Answer:

Option B is correct.

Step-by-step explanation:

Curved surface area of sphere:

$CSA= 4\pi \: {r}^{2}$

Let the radius of sphere1 is r1 and of sphere2 is r2

given in the question

$\frac{r_1}{r_2} = \frac{2}{5}$

Ratio of CSA of two spheres

$\frac{CSA_1}{CSA_2} = \frac{4\pi \: {r_1}^{2} }{4\pi \: {r_2}^{2} } \\ \\ \frac{CSA_1}{CSA_2} = \bigg({ \frac{r_1}{r_2} }\bigg)^{2} \\ \\ \frac{CSA_1}{CSA_2}= \bigg({ \frac{2}{5} }\bigg)^{2} \\ \\\frac{CSA_1}{CSA_2} = \frac{4}{25}$

Ratio of their curved surfaces areas is 4:25

Hope it helps you.