Question : A solid right circular cylinder and solid hemisphere stand on equal bases and have the same height. The ratio of their whole surface area is:
Option 1: 3 : 2
Option 2: 3 : 4
Option 3: 4 : 3
Option 4: 2 : 3
Correct Answer: 4 : 3
Solution :
Let the radius of the base as $r$ and the height of the cylinder and hemisphere as $h$.
The total surface area of a right circular cylinder $=2\pi r(r+h)$
The total surface area of a hemisphere $=3\pi r^{2}$
Given that the cylinder and hemisphere stand on equal bases and have the same height, such that $r = h$.
Substituting $r = h$ into the formulas,
The total surface area of the cylinder = $2\pi r(r+r) = 4\pi r^{2}$
The total surface area of the hemisphere = $3\pi r^{2}$
The ratio of their whole surface area $=4\pi r^{2}: 3\pi r^{2} = 4:3$
Hence, the correct answer is 4 : 3.
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