Question

A metallic sphere of radius 3 cm is dropped in a right circular cylindrical vessel partly filled with water, whose radius is 6 cm. lf the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

• A. 0.5 cm
• B. 1 cm
• C. 1.5 cm
• D. 2 cm

Answer 1

The correct option is B

1 cm

Let the level of water be raised by h cm.
Volume of the sphere dropped in the cylindrical vessel $=\frac{4}{3}\pi (3{)}^{2}c{m}^3$
$=\frac{4\pi \times 27}{3}c{m}^3$
$=36\pi c{m}^3$
Radius of the cylindrical vessel = 6 cm
Then, volume of the cylinder of radius 6 cm and height h cm $=\pi \times 6^2\times hc{m}^3$
$=36\pi hc{m}^3$
According to question,
Volume of the sphere dropped = Volume of the cylinder of radius 6 cm and height h cm
$\Rightarrow 36\pi c{m}^3=36\pi hc{m}^3$

$\Rightarrow h=\frac{36\pi }{36\pi }\Rightarrow h=1cm$
Hence, the level of water is raised by 1 cm.