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? [4 MARKS]

Answer 1

Formula: 1 Mark
Application: 1 Mark
Solution: 2 Marks
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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 $=\pi \times 6^2\times hc{m}^3$
$=36\pi hc{m}^3$
$\Rightarrow h=\frac{36\pi }{36\pi }\Rightarrow h=1cm$
Hence, the level of water is raised by 1 cm.