Chapter: Mensuration· Mathematics Part 2 (Geometry)
Answer: (i) 21% (ii) 33.1%
Let the original radius be r. New radius \(= r + \dfrac{10}{100}r = 1.1r\).
(i) New surface area \(= 4\pi (1.1r)^2 = 1.21 \times 4\pi r^2\). Increase \(= 0.21 \times 4\pi r^2\), i.e. 21% of the original.
(ii) New volume \(= \dfrac{4}{3}\pi (1.1r)^3 = 1.331 \times \dfrac{4}{3}\pi r^3\). Increase \(= 0.331 \times \dfrac{4}{3}\pi r^3\), i.e. 33.1% of the original.
Note: surface area changes as the square of the radius and volume as the cube, so the percentage increase is not 10% in either case.