SOLUTION: Two cylindrical containers are shown. Container A has a radius r and a height of h and holds a maximum of 100 ounces of water. Container B has a radius of 4r and a height of 12 h

Question 967724: Two cylindrical containers are shown. Container A has a radius r and a height of h and holds a maximum of 100 ounces of water. Container B has a radius of 4r and a height of 12 h .

What is the maximum amount of water that Container B can hold?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Two cylindrical containers are shown. Container A has a radius r and a height of h and holds a maximum of 100 ounces of water. Container B has a radius of 4r and a height of 12 h .

formula for volume of container A is v1 = pi * r^2 * h.

formula for volume of container B is v2 = pi * (4r)^2 * 12h.

simplify formula for container B to get v2 = pi * 16 * r^2 * 12 * h.

simplify further to get v2 = 192 * pi * r^2 * h.

you have v1 = pi * r^2 * h.
you have v2 = 192 * pi * r^2 * h.

the volume for container B is 192 times the volume for container A.

if container A holds 100 ounces of water, then container B should contain 192 * 100 ounces of water which would then be equal to 19,200 ounces of water.

this assumes the ratio of ounces to volume remains the wame.

100 / v1 = x / (192 * v1)

cross multiply to get 100 * 192 * v1 = x * v1

divide both sides of that equation by v1 to get 100 * 192 = x.

solve for x to get x= 19,200 ounces.

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