Question

If a solid sphere and a solid hemisphere have the same volume then the ratio of their total surface areas is

• A. $2:1$
• B. $\sqrt[3]{316}:3$
• C. $8:3$
• D. $\sqrt[3]{316}:2$

Answer 1

The correct option is A $2:1$

The volume of a sphere is $\frac{4}{3}\pi r^3$ and the volume of a hemisphere is $\frac{\frac{4}{3}\pi r^3}{2}$
Area of a sphere $=4\pi r^2$ and a hemisphere would be in simple terms half that of the sphere thus $2\pi r^2$
Supposing the sphere had a volume of $8$ and the hemisphere had a volume of $8$ then it has a ratio of $2:1$
Supposing the sphere has an area of 8 and the hemisphere also has an
area of $8.$ Then if the hemisphere was transposed to a complete sphere
then its area would be $16$ or twice that of the smaller sphere. The ratio
would then be $2:1$