A cylindrical vessel of diameter 32 cm is partially filled with water. A solid metallic sphere of radius 12 cm is dropped into it. What will be the increase in the level of water in the vessel (in cm) ?
Answer & explanation
Correct answer: option 1
We know that,
The volume of a cylinder = π × (Radius)2 × (Height)
The volume of a sphere = \(\frac{4}{3}\)π (Radius)3
We have,
The diameter of the cylindrical vessel = 32 cm
The radius of the solid metallic sphere = 12 cm
The radius of the cylindrical vessel = \(\frac{32}{2}\) = 16 cm
Let, the height of water increase = a cm
So, π × (16)2 × a = \(\frac{4}{3}\) × π × (12)3
= 256a = 2304
= a = 9