The length of the base of a box is 5 inches more than its width (w). The height of the box is 2 inches more than its width. Write an expression that represents the volume of the box.
To find the expression representing the volume of the box, we need to multiply its length, width, and height.
Given that the length of the base is 5 inches more than its width (w), we can write the length as w + 5.
Similarly, the height of the box is 2 inches more than its width (w), so the height can be represented as w + 2.
Therefore, the volume (V) of the box can be expressed as:
V = length × width × height
V = (w + 5) × w × (w + 2)
Therefore, the expression representing the volume of the box is (w + 5)w(w + 2).
To find an expression that represents the volume of the box, we need to determine the dimensions of the box first.
Let's assume the width of the box is "w" inches.
According to the given information, the length of the base is 5 inches more than its width. So, the length would be (w+5) inches.
Also, the height of the box is 2 inches more than its width. So, the height would be (w+2) inches.
The volume of a rectangular box is calculated by multiplying its length, width, and height.
Therefore, the expression that represents the volume of the given box is: (w+5) * w * (w+2).
So, the volume of the box is (w+5)(w)(w+2) cubic inches.
L = W + 5
H = W + 2
V = L * W * H
V = ( W + 5 ) * W * ( W + 2 )
V = ( W + 5 ) * ( W + 2 ) * W
V = ( W * W + 5 * W + 2 * W + 2 * 5 )
V = ( W ^ 2 + 5 W + 2 W + 10 ) * W
V = ( W ^ 2 + 7 W + 10 ) * W
V = W ^ 2 * W + 7 W * W + 10 * W
V = W ^ 3 + 7 W ^ 2 + 10 W