Question

If surface area of a sphere of radius “R” is equal to curved surface area of a hemisphere of radius “r”, what is the value of R/r ?

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. 2
• D. $\sqrt{2}$

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

We know that surface area of a sphere of radius “R” is given by $4\pi R^2$ and curved surface area of hemisphere of radius “r” is equal to $2\pi r^2$.

It is given that surface area of a sphere of radius “R” is equal to curved surface area of a hemisphere of radius “r”.

Hence, $4\pi R^2=2\pi r^2$
$2R^2=r^2$

Taking square roots on both sides we get,
$\sqrt{2}R=r$
$\frac{R}{r}=\frac{1}{\sqrt{2}}$

Therefore, option b is correct.