If the radius of a sphere is increased by 5%, then by what percentage will the surface area of the sphere increase?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 10.25%.
The surface area of a sphere = 4πr2, where r is the radius.
Let the original radius be r units.
The original surface area = 4πr2
If the radius is increased by 5%, the new radius = 105r/100 = 1.05r
The new surface area = 4π(1.05r)2 = 4π(1.1025r2) = 4.41πr2
Percentage of increase = [(New surface area - Original surface area)/Original surface area] × 100
= [(4.41πr2 - 4πr2)/4πr2] × 100
= (0.41πr2/4πr2) × 100
= 0.1025 × 100
= 10.25%
Therefore, the surface area of the sphere will increase by 10.25%.