A glass cylinder with A diameter 12 cm has initial water level at 120 cm. When a ball I totally immersed in it,the water level rises to 135 cm. What is the volume of the ball immersed?
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To find the volume of the ball immersed in the water, we need to calculate the difference in water levels before and after immersing the ball.
Given:
Diameter of the glass cylinder = 12 cm
Initial water level = 120 cm
Water level after immersing the ball = 135 cm
Step 1: Calculate the radius of the glass cylinder.
The radius is half the diameter, so the radius of the glass cylinder is 12 cm / 2 = 6 cm.
Step 2: Calculate the volume of water displaced when the ball is immersed.
The volume of water displaced is equal to the difference in the water levels before and after immersing the ball.
Initial water level - Water level after immersing the ball = 120 cm - 135 cm = -15 cm (negative value indicates a decrease in water level)
Step 3: Calculate the volume of the ball.
The volume of water displaced is equal to the volume of the ball. Thus, to find the volume of the ball, we need to find the volume of water displaced.
Using the formula for the volume of a cylinder: V = πr^2h
Volume of water displaced = π(6 cm)^2(-15 cm) ≈ -1696 cm^3 (negative value indicates a decrease in volume)
In this case, the volume of the ball immersed is approximately 1696 cm^3.