the width of a square-based storage tank is 3m less than its height. The tank has a capacity of 20m^3. If the dimensions are integer values in metres, what are they?
each side of base --- x m
height --- x+3
x^2(x+3) = 20
x^3 + 3x^2 = 20
since the solution is to be an integer, try
x=1 , 1 + 3 = 20 , no
x=2, 8 + 3(4) = 20 ,YES
well, that was easy.
base is 2 m by 2, with a height of 5
but its less than 3
base is 2 m by 2 m
height is 2+3 = 5 m
volume = 2x2x5 = 20
My answer is correct.
what do you mean by "but its less than 3"
oh nothing , i get it now, thank you :)
Well, well, it seems we have a math problem here! Let's see what we can do.
Let's call the height of the tank "h" meters. According to the problem, the width is 3 meters less than the height, so the width would be (h - 3) meters.
We know that the volume of a square-based storage tank can be calculated by multiplying the length, width, and height.
In this case, since it's a square-based tank, the length would be the same as the width, which is (h - 3) meters.
So we can set up an equation to find the value of h:
(h - 3) * (h - 3) * h = 20m^3
Now all we need is some good old-fashioned algebra to solve the equation. However, I must warn you, I might not have the most square sense of humor!
*cue circus music*
After some solving, we find that the height of the tank is 5 meters. Therefore, the width would be 2 meters (since 5 - 3 = 2). And both the length and width would be 2 meters.
So the dimensions of the tank are 5m x 2m x 2m.
Ta-da!
To find the dimensions of the square-based storage tank, we can set up the equation based on the given information.
Let's assume the height of the tank is "h" meters. According to the information, the width of the tank is 3 meters less than its height, which can be expressed as "h - 3".
Since the tank is square-based, the length, width, and height are all equal.
We know that the capacity of the tank is 20 cubic meters. The volume of a square-based storage tank can be calculated by multiplying the height by the width by the length. So, we have:
Volume = height × width × length
20 = h × (h - 3) × h
Simplifying the equation, we get:
20 = h^3 - 3h^2
To solve this equation, we can try different integer values for "h" until we find the one that satisfies the equation.
Let's make a table of values to evaluate the equation:
h | h^3 - 3h^2
---------------
1 | -2
2 | 4
3 | 0
4 | 16
By examining the values, we can see that when h = 3, the equation is satisfied.
Therefore, the height of the tank is 3 meters. Since the width is 3 meters less than the height, the width would be 3 - 3 = 0 meters.
However, it is not possible to have a width of 0 meters for a square-based storage tank, so it seems there is no integer solution for this problem.