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,width and height.
Let's use variables to represent the dimensions of the tank. Let the width be x cm, the height be 2x cm, and the depth be (x-4) cm.
To find the volume of the tank, which is given as 1440 cm^3, we use the formula: volume = length × width × height.
1440 = length × x × 2x × (x-4)
Simplifying the equation:
1440 = 2x^3 (x-4)
Dividing both sides by 2:
720 = x^3 (x-4)
Expanding the expression:
720 = x^4 - 4x^3
Rearranging the equation:
x^4 - 4x^3 - 720 = 0
This equation is a quartic equation, but it can be factored:
(x - 12)(x + 12)(x - 6)(x + 6) = 0
We can solve for the possible values of x:
x - 12 = 0 --> x = 12
x + 12 = 0 --> x = -12 (rejected since dimensions cannot be negative)
x - 6 = 0 --> x = 6
x + 6 = 0 --> x = -6 (rejected since dimensions cannot be negative)
Therefore, the width of the tank can be 12 cm or 6 cm. However, since the height is stated to be twice the width, we choose the width to be 6 cm.
Width = 6 cm
Height = 2 * Width = 2 * 6 cm = 12 cm
Depth = Width - 4 = 6 cm - 4 cm = 2 cm
Therefore, the dimensions of the tank are Length = arbitrary, Width = 6 cm, Height = 12 cm, and Depth = 2 cm.
Let's assume the width of the rectangular 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 m less than the width. Since 1 m is equal to 100 cm, the depth of the tank is (x - 400) cm.
The volume of the tank is given as 1440 cm^3.
To find the length of the tank, we will use the formula for volume: length * width * height = volume.
Plugging in the given values, we get:
length * x * 2x = 1440
2x^3 = 1440
Dividing both sides of the equation by 2, we get:
x^3 = 720
To find the value of x, we can take the cube root of both sides:
x = ∛(720)
Using a calculator, we find that x ≈ 9.2
Therefore, the width of the tank is approximately 9.2 cm.
Since the height is twice the width, the height of the tank is 2 * 9.2 = 18.4 cm.
And the depth of the tank is 4 m less than the width, which is 9.2 - 4 = 5.2 cm.
So, the dimensions of the tank are:
Length ≈ Unknown
Width ≈ 9.2 cm
Height ≈ 18.4 cm
Depth ≈ 5.2 cm