If the radius of a sphere is increased by 50%, then its surface area will increase by:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 125%
The surface area of a sphere is \(4\pi r^2\), so it varies as the square of the radius: if the radius is multiplied by a factor, the area is multiplied by the square of that factor.
New radius \(=1.5r\)
New area \(=4\pi(1.5r)^2=2.25\times4\pi r^2\)
Increase \(=2.25-1=1.25\) times the old area, that is, 125%
Shortcut: For two successive increases of \(a\%\) and \(b\%\) the total increase is \(\displaystyle a+b+\frac{ab}{100}\). The area takes the 50% increase twice: \(\displaystyle 50+50+\frac{50\times50}{100}=125\%\).