A closed cylindrical tank contains 36(pi) cubic feet of water and is filled to half its capacity. When he ank is placed upright on its circular base on level ground, the height of the watr in the tank is 4 feet. Whn the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?
A) 2
B)3
C)4
D)6
E)9
2006-10-02 04:34:55 · 4 answers · asked by Anonymous in Education & Reference ➔ Higher Education (University +)
First you have to find the radius of the cylinder. Since it is only half full, you know that the total volume is 72(pi) and the equation for the volume of a cylinder is pi*r*r*h.
Solve for r and you get 3 ft, so the radius is 3 ft.
Now looking at the link I gave you (toward the bottom) you see an ugly looking equation. If you set the radius equal to "h" you end up with V(h=r) = pi*r*r*L/2 = pi*3*3*8/2 = 36(pi) which is what the water volume is, so the radius is equal to "h" which is 3 ft. (answer is B) The eight comes from twice the height of the water at 4 ft. I set "h" equal to the radius just to see if it matched the volume, which it did.
If it was more or less than the radius, you would have to solve for "h" and plug everything else in since you have all the other values. The reason it is exactly half full is so you can use the "h" = radius substitution or just be able to set "h" to the radius (as the answer) since a cylinder is symmetrical (so you can probably ignore the long ugly looking equation and just say that "h" is equal to the radius).
Just a note about the first two answers...the first answer basically says that the height of the water is 6 ft, which means that the water level is all the way to the top of the cylinder since it it laying on its side and the radius is 3 ft (doesn't make sense). And the second answer didn't factor in pi (3.14159) so 1.7 is not the right answer either
2006-10-02 05:05:54 · answer #1 · answered by paisak79 3 · 1⤊ 0⤋
A tank that is 1/2 filled upright will be 1/2 filled on its side also. The total volume of the tank is 72 cf. On its side, the water level will be 1/2 way up the tank, which is 1/2D or R. Using cylindrical volume = pi*rsquared*h, r is equal to 1.7. Closest answer would be A) 2.
2006-10-02 11:51:34 · answer #2 · answered by Leader Desslok 4 · 0⤊ 1⤋
The volume of a cylindar is pi*r^2 * length
Length is 4, volume is 36*pi. -- so
pi * r^2 * 4 = 36 * pi
divide by 4*pi to get
r^2 = 9
r = 3
Diameter = 2*r -- so D (6) is the right answer.
2006-10-02 11:42:44 · answer #3 · answered by Ranto 7 · 1⤊ 1⤋
Go with paisak79. He's right, the first two answers were wrong.
2006-10-02 14:11:02 · answer #4 · answered by bh8153 7 · 0⤊ 0⤋