Q178
ArithmeticGeometry & Mensuration
A cylindrical vessel of radius 4cm contains water. A solid sphere of radius 3cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by
- a.$\frac{2}{9}$ cm
- b.$\frac{4}{9}$ cm
- c.$\frac{9}{4}$ cm
- d.$\frac{9}{2}$ cm
Answer: (C) $\frac{9}{4}$ cm
The sphere displaces $\frac{4}{3}\pi \times 3^3 = 36\pi$ cm³ of water. Spread over the base $\pi \times 4^2 = 16\pi$ cm², the rise is $\frac{36}{16} = \frac{9}{4}$ cm. Option B inverts this fraction.