Question

the ratio of radii of two spheres is 3:5. then ,the ratio of their surface area is ​

Answer 1

ANSWER:-

Given:

The ratio of radii of two sphere is 3:5.

To find:

Find their surface area.

Solution:

Let the diameter of two sphere are d1&d2, respectively.

So,

d1 : d2= 3:5

Therefore,

We know that surface area of the sphere is;

=) 4πr²

Now,

Ratio of their surface areas;

$= > \frac{4\pi {r}^{2} 1}{4\pi {r}^{2}2 } \\ \\ = > \frac{(2r1) { }^{2} }{(2 r2) {}^{2} } = \frac{d1}{d2} \\ \\ = > ( \frac{d1}{d2} ) {}^{2} = ( \frac{3}{5} ) {}^{2} = \frac{9}{25} \\ \\ = > 9 \ratio 25$

Hence,

Surface area in ratio, 9:25.

Hope it helps ☺️

Answer 2

Answer:

$A_{1} : A_{2} = 9 : 25$

Step-by-step explanation:

Given the ratio of radius of two sphere is 3 : 5

Let R : r = 3 : 5

$\dfrac{R}{r} = \dfrac{3}{5}$

Where R is radius of first sphere

And r is the radius of second sphere.

We know the surface area of a sphere

A = $4 \pi \times R^{2}$

Let $A_{1}$ is the area of first sphere and $A_{2}$ is the area of send sphere

$A_{1}  = 4\pi R^{2}$

$A_{2} = 4\pi r^{2}$

$\dfrac{A_{1} }{A_{2} }$ = $\dfrac{4\pi R^{2} }{4\pi r^{2}}$

                                                = $\dfrac{R^{2} }{r^{2} }$

                                                =  $[\dfrac{R}{r}] ^{2}$

                                                = $[\dfrac{3}{5}]^{2}$

                                                = $\dfrac{9}{25}$

$A_{1} : A_{2} = 9 : 25$