Problema Solution
After 2 ,minutes of filling a 5 gallon pail, the water is 71/2inches high. Shelia wants the level of the water in the pail to be 12 inches high. Write an equation shelia could solve to find out how many more inches of water she needs to add to the pail?
Answer provided by our tutors
1 gallon = 231 cubic in^3
V = 5 gallons = 5*231 in^3
The water is h1 = 7 1/2 = (7*2+1)/2 = 15/2 in
h2 = 12 in
Sheila want the water to be 12 inches high and lets consider the pail to be cylinder.
By the volume formula of cylinder we get that the Ares of the base of the cylinder B is
B * h1 = V
B = V/h1
B = 231 / (15/2) = 462/15 in^2
V2 = B * h2 = (V/h1)*h2 = V*h2 / h1
The difference in in^3 will be V2 - V = V*h2 / h1 - V = (h2/h1 - 1) in^3
The difference in hight is h2 - h1 = 12 - 15/2 = 9/2 = 4.5 in