Question

the ratio of the surface areas of the two spears is 16 : 49 the ratio of their radii is​

Answer 1

Let’s get this problem solved......

Let the radius of the two spheres be r and R respectively in correspondence to the question

We know that the surface area of a sphere is :

SA = 4 x pi x radius^2

Therefore,

16/49 = (4 x pi x r^2)/(4 x pi x R^2)
16/49 = r^2 / R^2

Therefore,

r : R = 4 : 7

Hope it will help you!!!
P.S.: Here, ‘^’ means to represent exponent. For eg.:

X^Y means Y is the exponent of X

Answer 2

The ratio of the radii of the two spheres will be 4 : 9.

Given:

the ratio of the surface area of two spheres is = 16 : 49

To Find:

the ratio of the radii of the two spheres

Solution:

let the radii of the two spheres be r₁ and r₂

we know that the surface area of a sphere is = 4πr²

thus, we get the following equation-

4πr₁² : 4πr₂² = 16 : 49

⇒ r₁² : r₂² = 16 : 49

or r₁² / r₂² = 16 / 49

r₁ / r₂ = √(16 / 49)

r₁ / r₂ = 4 / 9

Thus, the ratio of the radii of the two spheres will be 4 : 9.

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