Question: A rectangular prism shaped produce drawer in a refrigerator is 8 inches tall. The perimeter of the bottom of the drawer is 48 inches. The length of the bottom of the drawer is 4 inches longer than the width. Find the volume of rectangular prism shape.
Answer:
1120 cubic inch
Explanation:
Applying
V = Ah................... Equation 1
Where v = volume, A = Area of the base, h = height.
Note: The prism has a rectangular base,
Therefore,
A = l×w
A = lw................... Equation 2
Where l = lenght of the rectangle, w = width of the rectangle.
Substitute Equation 2 into equation 1
V = lwh................. Equation 3
Also
P = 2(l+w).................. Equation 4
From the question,
l = w+4 (the length of the bottom of the drawer is 4 inches longer than the width), P = 48 inches.
Substitute these values into equation 4
48 = 2(w+4+w)
2(w+4+w) = 48
(w+4+w) = 48/2
(w+4+w) = 24
2w+4 = 24
2w = 24-4
2w = 20
w = 20/2
w = 10 inches, l = 10+4 = 14 inches.
Also given: h = 8 inches.
Substitute these values into equation 3
V = 10×14×8
V = 1120 cubic inch