a rectangular box is to be constructed with its length four times the size of
its width, and its height one half the size of its length. the volume of the box
must be 1000 cubic centimeters. find the dimensions of the box
V = WxLxH
L = 4W
H = L/2 = 2W
1000 = Wx4Wx2W = 8W3
125 = W3
W=5
I assume you can work out the other dimensions
Let's assume the width of the box is W cm.
Given that the length of the box is four times the width, it can be represented as 4W cm.
Also, the height of the box is one half the length, so it can be represented as (1/2) * 4W cm, which simplifies to 2W cm.
The volume of the box is given as 1000 cubic centimeters, so the equation becomes:
Volume = Length * Width * Height
1000 = (4W) * W * 2W
Let's simplify the equation:
1000 = 8W^3
Now, divide both sides of the equation by 8:
1000/8 = W^3
125 = W^3
To find the width (W), we can take the cube root of both sides:
∛125 = ∛W^3
5 = W
Now that we have the width, we can find the length and height:
Length = 4W = 4 * 5 = 20 cm
Height = 2W = 2 * 5 = 10 cm
Therefore, the dimensions of the box are:
Width = 5 cm
Length = 20 cm
Height = 10 cm
To find the dimensions of the box, we can use the given information and work step by step.
Let's start by assigning variables to the dimensions of the box.
Let:
Width = W
Length = 4W (as given)
Height = (1/2)(4W) = 2W (as given)
Now, let's use the formula for the volume of a rectangular box, which is length × width × height:
Volume = Length × Width × Height
Substituting the given values into the formula, we have:
1000 = (4W) × W × 2W
Simplifying the equation, we get:
1000 = 8W^3
To solve for W cubed, divide both sides of the equation by 8:
W^3 = 1000 / 8
W^3 = 125
Now, we need to find the cube root of 125 to get W:
W = ∛125
W = 5
Therefore, the width of the box is 5 centimeters.
Next, we can find the length and height by substituting the value of W into our previously assigned expressions:
Length = 4W = 4 * 5 = 20 centimeters
Height = 2W = 2 * 5 = 10 centimeters
So, the dimensions of the box are:
Width = 5 centimeters
Length = 20 centimeters
Height = 10 centimeters