Question

A cylindrical cistern whose radius is 7 cm is partly filled with water. If a conical block of iron whose radius of the base is 3.5 cm and height is 6 cm is wholly immersed in the water, by how much will the water level rise? $(Use\pi =\frac{22}{7})$ [4 MARKS]

Answer 1

Formula Framing: 2 Marks
Application: 1 Mark
Solution: 1 Mark

According to question,
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.