A right circular cylinder is partially filled with water. A solid meta

1.	A right circular cylinder is partially filled with water. A solid metallic spherical ball is dropped in the cylinder. The radius of the sphere is 2.1 cm and the radius of the cylinder is 7 cm. Find the rise in water level after the bass is dropped?1. 0.292 cm2. 0.232 cm3. 0.286 cm4. 0.252 cm
Answer» Correct Answer - Option 4 : 0.252 cm Given: Radius of spherical ball(R) = 2.1 cm Radius of cylinder(r) = 7 cm Concept: The volume of the ball will the volume of the water displaced. So, the volume of the cylindrical part with rise in water level will be equal to the volume of the ball. Formula used: Volume of sphere = (4/3)πr³ Volume of cylinder = πr²h Calculation: Let, the rise in water level = h cm ∵ Volume of sphere = Volume of cylinder ⇒ (4/3)πR³ = πr²h ⇒ (4/3) × 2.1 × 2.1 × 2.1 = 7 × 7 × h ⇒ h = (4 × 2.1 × 2.1 × 2.1)/(3 × 7 × 7) ⇒ h = 0.252 cm

A right circular cylinder is partially filled with water. A solid metallic spherical ball is dropped in the cylinder. The radius of the sphere is 2.1 cm and the radius of the cylinder is 7 cm. Find the rise in water level after the bass is dropped?1. 0.292 cm2. 0.232 cm3. 0.286 cm4. 0.252 cm

Answer» Correct Answer - Option 4 : 0.252 cm

Given:

Radius of spherical ball(R) = 2.1 cm

Radius of cylinder(r) = 7 cm

Concept:

The volume of the ball will the volume of the water displaced. So, the volume of the cylindrical part with rise in water level will be equal to the volume of the ball.

Formula used:

Volume of sphere = (4/3)πr³

Volume of cylinder = πr²h

Calculation:

Let, the rise in water level = h cm

∵ Volume of sphere = Volume of cylinder

⇒ (4/3)πR³ = πr²h

⇒ (4/3) × 2.1 × 2.1 × 2.1 = 7 × 7 × h

⇒ h = (4 × 2.1 × 2.1 × 2.1)/(3 × 7 × 7)

⇒ h = 0.252 cm

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