Question

The ratio of the total surface areas of two solid hemisphere is 25 : 16 then ratio of their volumes will be

• A. $5:4$
• B. $125:64$
• C. $27:16$
• D. $81:64$

Answer 1

The correct option is B $125:64$

Total Surface Area of a hemisphere of radius 'r' $=3\pi r^2$

Let $r_1$ be the radius of the first hemi sphere and $r_2$ and be the
radius of the second hemi sphere.

Now, ratio of their surface areas is:
$S_1:S_2=25:16$
$=3\pi {r_1}^2:3\pi {r_2}^2=25:16$
$={r_1}^2:{r_2}^2=25:16$
$=>r_1:r_2=5:4$

Volume of a hemisphere of radius 'r' $=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\pi {r_1}^3:\frac{2}{3}\pi {r_3}^2$
$={r_1}^3:{r_2}^3$
$=5^3:4^3$

$=125:64$