Question

A cylindrical vessel $60$ cm in diameter is partially filled with water. A sphere, $54$ cm in diameter is gently dropped into the vessel. To what further height will water rise in the cylinder?

• A. $20.02$ cm
• B. $30.29$ cm
• C. $29.16$ cm
• D. $25$ cm

Answer 1

Answer: (C)

$29.16$ cm

Lets analyse the situation,

Since the sphere increases the volume of water, this increase in volume will be equal to the volume of the sphere dropped.
This increased volume can be seen as a cylinder itself shown in light blue color.
Now, lets assume that the increase in height=h
Thus we can write:

$\pi {r_1}^{2}h=\frac{4}{3}\pi {r_2}^3,\text{where}$ $r_1$=radius of cylinder, $r_2=$radius of sphere

$h=\frac{4{r_2}^3}{3r_1^2}=\frac{4\times 27\times 27\times 27}{3\times 30\times 30}=29.16$ cm