A cylindrical glass is of capacity 100 cubic centimetre. If the radius of the glass is increased by two times of the original radius of that glass, then the capacity of the glass will be

Correct Answer: (D) 900 cubic centimetre

The volume of a cylindrical glass is $V =$$\pi$ r^2 h = 100 $\text{ cm}$^3. When the radius is increased by two times the original radius, the new radius becomes $R = r + 2r = 3r$. Since volume is proportional to the square of the radius, the new capacity is $\pi (3r{)}^{2}h=9\pi r^{2}h=9\times 100=900{\text{ cm}}^3$$\pi$ (3r)^2 h = 9 $\pi$ r^2 h = 9 $\times$ 100 = 900 $\text{ cm}$^3.