SOLUTION: A cylindrical container has a base area of 100 cm^2 and is 12 cm high. If the container is one-third filled with water, what is the volume of the water in the container?

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Question 150915: A cylindrical container has a base area of 100 cm^2 and is 12 cm high. If the container is one-third filled with water, what is the volume of the water in the container?
Found 2 solutions by vleith, jojo14344:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of a cylinder is given by
V+=+pi%2Ar%5E2%2Ah
We are given the area of the base pi%2Ar%5E2 and the height
Our cylinder is 1/3 full.
So
v+=+100%2A12%2F3
v+=+400 cubic centimeter

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
We know the in finding the Volume of the container = pi%28r%5E2%29h
The height is given which is %281%2F3%29%2812cm%29, but we don't have the radius, r.
Since Area is given, we can get it there, with the formula,
A=2pi%28r%5E2%29%2B2pi%28r%29h---- area on the top and base + area on the sides
100=2pi%28r%5E2%2B%28rh%29%29
%28100%2F2pi%29=r%5E2%2Brh
Substituting & re-arranging,
r%5E2%2B12r-%2850%2Fpi%29=0
by Quadratic eqn, x=r, a=1, b=12,c=+-50%2Fpi
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x=%28-12%2B-sqrt%2812%5E2-4%2A1%2A-50%2Fpi%29%29%2F%282%2A1%29
x=%28-12%2B-sqrt%28144%2B200%2Fpi%29%29%2F2
x=%28-12%2B-sqrt%28207.66198%29%29%2F2
x=%28-12%2B-14.41%29%2F2
x=%28-12%2B14.41%29%2F2-----> x=1.205
x=%28-12-14.41%29%2F2-----> x=-13.205
USE x=1.205=r
So V=pi%281.205%5E2%29%2812%2F3%29
V=5.81%28pi%29cc
Thank you,
Jojo