A cylindrical tank with a radius of 7 cm contains water up to a height of 40 cm. After a solid spherical ball with a radius of 7 cm is completely submerged in the tank, what will be the new water height?
Show answer & explanation
Correct answer: D
Explanation
Given:
Radius of the cylinder = 7 cm
Initial height of the water = 40 cm
Radius of the ball = 7 cm
Formula:
Volume of the cylinder = πr²h
Volume of the sphere = (4/3)πr³
Volume of the sphere = (4/3)π(7)³ = 1372π/3
Base area of the cylinder = π(7)² = 49π
Increase in height of the water = (1372π/3) / 49π = 28/3 cm
New height = 40 + 28/3 = 49.33 cm