Question : The radius of a hemisphere is twice that of a sphere. What is the ratio of the total surface area of the hemisphere and sphere?
Option 1: 3 : 1
Option 2: 12 : 1
Option 3: 4 : 1
Option 4: 6 : 1
Correct Answer: 3 : 1
Solution :
The total surface area of a sphere with radius r,
$⇒\text{TSA}_1 = 4\pi r^2$
The total surface area of a hemisphere with radius R,
$⇒\text{TSA}_2 = 3\pi R^2$
Given that the radius of the hemisphere is twice that of the sphere, ($R = 2r$).
$⇒\text{TSA}_2 = 3\pi (2r)^2 = 12\pi r^2$
The ratio of the total surface area of the hemisphere to the sphere.
$⇒\frac{\text{TSA}_2}{\text{TSA}_1} = \frac{12\pi r^2}{4\pi r^2} = 3$
Hence, the correct answer is 3 : 1.
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