Question

Radii of two solid hemispheres are in the ratio 3:5. Find the ratio of their curved surface areas.

• A. $\frac{C_1}{C_2}$ = $\frac{2}{25}$
• B. None of these
• C. $\frac{C_1}{C_2}$ = $\frac{9}{5}$
• D. $\frac{C_1}{C_2}$ = $\frac{9}{25}$

Answer 1

The correct option is D $\frac{C_1}{C_2}$ = $\frac{9}{25}$

Correct option is (A).

Given that,
Radii of two solid hemisphere are in ratio = 3 : 5
<!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> $\frac{r_1}{r_2}$ = <!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> $\frac{3}{5}$
We know that ,
$\frac{C.S.Aofsphere\left(1\right)}{C.S.Aofsphere\left(2\right)}$ = $\frac{4\pi r_1^2}{4\pi r_2^2}$
$\frac{C.S.Aofsphere\left(1\right)}{C.S.Aofsphere\left(2\right)}$ = $\frac{r_1^2}{r_2^2}$
$\frac{C.S.Aofsphere\left(1\right)}{C.S.Aofsphere\left(2\right)}$ = $\frac{3^2}{5^2}$
$\frac{C.S.Aofsphere\left(1\right)}{C.S.Aofsphere\left(2\right)}$ = $\frac{9}{25}$

Answer : $\frac{C_1}{C_2}$ = $\frac{9}{25}$