SOLUTION: A cylindrical can of internal radius 20 cm stands upright on a flat surface. It contains water to a depth of 20 cm. Calculate the rise in the level of the water when a brick of a
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Question 243261: A cylindrical can of internal radius 20 cm stands upright on a flat surface. It contains water to a depth of 20 cm. Calculate the rise in the level of the water when a brick of a volume of 1500cm^3 is immersed in the water.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
The brick increases the volume of the water by 1500cm^3.
The cylindrical can has an internal radius of 20cm.
It has water to a depth of 20 cm.
The volume of water in the cylinder is equal to pi * r^2 * h where:
h = 20 cm
r = 20 cm
Volume of water in the cylinder is pi * 20^2 * 20 = pi * 400 * 20 * cm^3.
This equals pi * 8000 * cm^3 which equals 25132.74123 * cm^3.
Add 1500 * cm^3 to that and you get a total of 26632.74123 * cm^3
The radius of the cylinder remains the same as 20 * cm.
The formula for the volume of the cylinder is the same (pi * r^2 * h)
Only the height can vary.
The formula becomes:
26632.74123 = pi * 400 * h
Divide both sides of this equation by pi * 400 to get:
26632.74123 * cm^3 / (pi * 400 * cm^2) = h
Solve for h to get:
h = 21.19366207 cm
The original height was 20 cm^3
The water level rose 1.193662073 * cm
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