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

Algebra ->  Volume -> 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      Log On


   

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) About Me  (Show Source):
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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