An open rectangular tank is made of steel plate of volume 1440cm cube it height is twice its width if the depth of the tank is 4 m less than width. Find its length
Let's assume the width of the tank is x cm.
Given that the height is twice the width, the height of the tank is 2x cm.
Also, the depth of the tank is 4 cm less than the width, so the depth is x-4 cm.
Volume of the tank = Length * Width * Depth
1440 = Length * x * (x-4)
Simplifying the equation:
1440 = x(x-4)(2x)
Expanding and combining like terms:
1440 = 2x^3 - 8x^2
Rearranging the equation:
2x^3 - 8x^2 - 1440 = 0
Dividing both sides by 2:
x^3 - 4x^2 - 720 = 0
To solve this equation, we can use trial and error or use a graphing calculator. The possible values for x are integers that divide 720, such as 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 144, 180, 240, 360, 720.
By trying some of these values, we find that x=12 satisfies the equation. Therefore, the width of the tank is 12 cm.
The height of the tank is 2x, so the height is 2*12 = 24 cm.
And the depth of the tank is x-4, so the depth is 12-4 = 8 cm.
Finally, the volume of the tank is length * width * depth. Substituting the values, we get:
1440 = length * 12 * 8
Simplifying:
1440 = 96 * length
Dividing both sides by 96:
length = 1440/96 = 15
Therefore, the length of the tank is 15 cm.
Let's assign variables to the width, height, and depth of the tank.
Let the width = w cm
Then, the height = 2w cm
And the depth = w - 4 cm
The volume of the tank is given as 1440 cm³. We can use this information to create an equation.
Volume = Width × Height × Depth
1440 = w * 2w * (w - 4)
Simplifying the equation:
1440 = 2w^2 * (w - 4)
1440 = 2w^3 - 8w^2
2w^3 - 8w^2 - 1440 = 0
Now we can solve this cubic equation to find the value of w.
However, solving cubic equations manually can be complex and time-consuming. Instead, let's use an online cubic equation solver to find the roots.
After solving the equation, we find that the width (w) is approximately 9.38 cm.
Since the length of the tank is not given directly, we need additional information or assumptions to determine the length.