Question

the ratio of suface areas of two spheres is 25:49. find the ratio between their radii

Answer 1

let the ratios of two radii are r, R

ratio of two surface areas = 25:49

4πr²/4πR² = 25/49

r²/R² = (5/7)²

(r/R)²= (5/7)²

r/R = 5/7
r:R =5:7

Answer 2

Step-by-step explanation:

Let the radius of two semicircles be $r_1$ and $r_2$

→ Given :-

▶ The ratio of areas of two semicircles = 49:25 .

$\begin{lgathered}= > \frac{a_1}{a_2} = \frac{49}{25} . \\ \\ = > \frac{ \frac{ \cancel\pi {r_1}^{2} }{ \cancel2} }{ \frac{ \cancel\pi {r_1}^{2} }{ \cancel2} } = \frac{49}{25} . \\ \\ = > {( \frac{r_1}{r_2}) }^{2} = \frac{49}{25} . \\ \\ = > \frac{r_1}{r_2} = \sqrt{ \frac{49}{25} } . \\ \\ = > \frac{r_1}{r_2} = \frac{7}{5} .\end{lgathered}$

→ To find :-

▶ The ratio of their circumference.

$\begin{lgathered}\therefore \frac{c_1}{c_2} \\ \\ = \frac{ \cancel\pi r_1}{ \cancel\pi r_2} . \\ \\ = \frac{r_1}{r_2} . \\ \\ = \boxed{ \green{ \frac{7}{5} .}}\end{lgathered}$

Hence, ratio of their circumference is 7 : 5 . ......