A cylindrical glass 7 cm in diameter and 10 cm tall is filled with water to a height of 9 cm.
If a ball 5 cm in diameter is dropped into the class and sinks to the bottom, will the water in the glass overflow
To figure out if the water will overflow, we need to calculate the volume of water in the glass before and after the ball is dropped in.
First, let's calculate the volume of water in the glass before the ball is dropped in:
Radius of the glass = 7/2 = 3.5 cm
Height of water in the glass = 9 cm
Volume of water = πr^2h = π(3.5)^2(9) = 110.25π cm^3
Now, let's calculate the volume of the ball:
Radius of the ball = 5/2 = 2.5 cm
Volume of the ball = 4/3πr^3 = 4/3π(2.5)^3 = 65.45π cm^3
Now, let's calculate the total volume of water and the ball in the glass after the ball is dropped in:
Total volume = Volume of water + Volume of ball = 110.25π + 65.45π = 175.7π cm^3
Now, let's calculate the new height of the water in the glass with the ball in it:
Let h be the new height of the water
π(3.5)^2h = 175.7π
h = 175.7/(3.5)^2
h = 14 cm
Since the height of the glass is 10 cm, the water will overflow when the ball is dropped in.