Question

The surface area of two hemisphere are in the ratio 25:49, find the ratio of their radii

Answer 1

Correct Question :

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

$\textbf {\underline {\underline {Step-By-Step\:Explanation:-}}}$

$\textbf {\underline {Given:}}$

• Surface area of 2 hemisphere are in the ratio 25:49

$\textbf {\underline{To\:Find:}}$

• The ratio of their radii

$\textbf {\pink {\underline {Formula\:Used:}}}$

• Surface area of hemisphere = $2\pi\:r^2$

$\huge\underline\green {\tt Solution:}$

Let the radius of first hemisphere be ' R '

and the radius of second hemisphere be ' r '

➡ The ratio of their surface area is 25:49

So,

$\dfrac {2\pi\:R^2}{2\pi\:r^2}= \dfrac {25}{49}$

➡ $\dfrac{R^2}{r^2} = \dfrac {25}{49}$

➡$\dfrac {R}{r} = \sqrt {\dfrac {25}{49}}$

➡$\dfrac {R}{r} = \dfrac {5}{7}$

= 5 : 7

Answer :

The ratio of their radii is 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 .