Question

A cylindrical cistern whose radius is 7 cm is partly filled with water. If a conical block of iron whose radius is 3.5 cm and height is 6 cm is wholly immersed in the water, by how much will the water level rise? $(Use\pi =\frac{22}{7})$

• A. 0.75 cm
• B. 1 cm
• C. 1.5 cm
• D. 0.5 cm

Answer 1

The correct option is D

0.5 cm

Let the water level rise by H cm.

Volume of water displaced in cylinder = Volume of conical block iron
$\therefore \pi R^{2}H=\frac{1}{3}\pi r^{2}h\Rightarrow 7\times 7\times H=\frac{1}{3}\times 3.5\times 3.5\times 6\Rightarrow H=\frac{1\times 3.5\times 3.5\times 6}{3\times 7\times 7}\Rightarrow H=0.5cm$
$\therefore$ Water level rises by 0.5 cm.