Question

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm partly filled with water. If the sphere is completely submerged, then the water level rises (in cm) by

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (A)

3

Radius of the sphere, $r_s=\frac{18}{2}$ cm = 9 cm

Radius of the cylinder, $r_c=\frac{36}{2}$ cm = 18 cm

Let the water level in the cylinder rises by h cm.

After the sphere is completely submerged.

Volume of the sphere = Volume of liquid raised in the cylinder

$\Rightarrow \frac{4}{3}\pi (r_s{)}^3=\pi (r_c{)}^2\times h$

$\Rightarrow \frac{4}{3}\pi (9cm{)}^3=\pi (18cm{)}^2\times h$

$\Rightarrow h=\frac{4\times 9\times 9\times 9}{3\times 18\times 18}cm$

$\Rightarrow h=3cm$

Thus, the water level in the cylinder rises by 3 cm.

The correct answer is C.