Question

Clare wants to make an open-top box by cutting out corners of a 28 inch by 20 inch piece of poster board and then folding up the sides. Which equation below represents V(x), the volume of the open-top box after making cutouts x inches long?

Answer 1

`\bold{ANSWER:}`
V = 560 - 4x^2


`\bold{SOLUTION:}`

• The volume of a rectangular prism is given by ⁠V = lwh, where "l" is the length, "w" is the width, and "h" is the height.

• How to solve? Find the original rectangle, then subtract the volume of the four cutouts to find the volume of the open-top box.

STEP 1: Find the volume of the original rectangle:

V = lwh

V = 28 • 20 • 1

V = 560

STEP 2: Find the volume of one cutout:

V = lwh

V = x • x • 1

V = x^2

STEP 3: Find the volume of the four cutouts:

V = 4x^2

STEP 4: Subtract the volume of the four cutouts from the volume of the original rectangle to find the volume of the open-top box:

V = 560 - 4x^2 — (ANS)