The ratio of the radius of Hemisphere A to Hemisphere B is 2:1.
If the curved surface area of Hemisphere A is equal to the volume of Hemisphere B, find the radius of Hemisphere B.

Correct option is A

Given
Ratio of radius of Hemisphere A to Hemisphere B = 2:1
Curved Surface Area (CSA) of Hemisphere A = Volume of Hemisphere B

Formula Used
CSA of Hemisphere = $$2\pi r^2$$​​
Volume of Hemisphere = $$\frac{2}{3}\pi r^3$$​​

Solution
Let the radius of Hemisphere B be r.
Then, the radius of Hemisphere A = 2r.
CSA of Hemisphere A =  $$2 \times \pi \times (2r)^2 = 8\pi r^2$$​​
Volume of Hemisphere B = $$\frac{2}{3}\pi r^3$$​​
Equating both as given in the question:
​$$8\pi r^2 = \frac{2}{3}\pi r^3$$​​

​$$4 = \frac{1}{3}r$$​​
r = 12 cm
Final Answer
So the correct answer is (a)