The area of the base of a rectangular juice box is 4 1/2 square inches. If the volume of the box is 18 cubic inches, how tall is the box?
Volume of rectangular box is length x width x height:
V = l*w*h
Area of the base is also length x width, so
V = (area of the base)*h
18 = (4.5)*h
h = 18 / 4.5
Its 4
I don’t get it how do you get 4.5?
its 3.5
To find the height of the box, we need to know the formula for the volume of a rectangular box, which is given by V = lwh, where V represents the volume, l represents the length, w represents the width, and h represents the height.
In this case, we are given that the volume of the box is 18 cubic inches. Thus, we have the equation 18 = lwh.
We are also given that the area of the base of the box is 4 1/2 square inches. The formula for the area of a rectangle is A = lw, where A represents the area, l represents the length, and w represents the width.
Substituting the given area into the equation, we have 4 1/2 = lw.
To simplify the calculations, let's convert the mixed number 4 1/2 into an improper fraction. 4 1/2 is equal to 9/2.
So, we now have the equation 9/2 = lw.
To solve for h, we need to isolate it in the volume equation. First, we can solve the area equation for either l or w. Let's solve for l.
Divide both sides of the equation 9/2 = lw by w:
(9/2) / w = l.
Now, substitute this expression for l in the volume equation:
18 = (9/2)w * h.
Multiply both sides of the equation by 2/9 to isolate the product of w and h:
(2/9) * 18 = w * h.
Simplifying the left side, we get:
4 = w * h.
Now, we have the equations h = (2/9) * 18 / w and w * h = 4.
Since we know that the volume of the box is 18 cubic inches, we can substitute this value into the equation w * h = 4:
18 = 4.
This equation tells us that w * h equals 4. Since the area of the base is 4 1/2, it's clear that w = 2 and h = 2.
Therefore, the height of the box is 2 inches.