Question

The surface area of two hemispheres are in the ratio 25 : 49. Find the ratio of their
radii.

Answer 1

Step-by-step explanation:

Given -

• Ratio of surface area of two hemisphere = 25/49

To Find -

Ratio of their radii

As we know that :-

• Surface area of hemisphere = 2πr²

Now,

» 2πr1²/2πr2² = 25/49

» (r1/r2)² = 25/49

» r1/r2 = √25/49

» r1/r2 = 5/7

Hence,

The value of Ratio of their radii is 5 : 7

Answer 2

QuEsTiOn :-

The surface area of two hemispheres are in the ratio 25 : 49. Find the ratio of their radii.

Given :-

• Surface area of two hemisphere are in the ratio 25:49.

To find :-

• Ratio of their radii.

Formula Used :-

Surface area of hemisphere = 2πr²

SoLuTiOn :-

Let the radius of 1st hemisphere is 'R' and Radius of 2nd hemisphere is 'r'.

According to question

$\implies \frac{2\pi {R}^{2} }{2\pi {r}^{2} } = \frac{25}{49} \\ \\ \implies \frac{ R}{ r } = \sqrt{ \frac{25}{49} } \\ \\ \implies \frac{R}{r} = \sqrt{ \frac{5 \times 5}{7 \times 7} } \\ \\ \implies \frac{R}{r} = \frac{5}{7}$

Therefore,

${\purple{\boxed{\large{\bold{The \: ratio \: of \: their \: radii = \frac{5}{7} }}}}}$