Question

A box is formed by cutting squares from the four corners of an 11"-wide by 15"-long sheet of paper and folding up the sides. Write a formula that expresses the volume of the box in cubic inches. A. V = 11x² + 15x² - 4x³

B. V = 11x + 15x - 4x³
C. V = 11x² + 15x² + 4x³
D. V = 11x + 15x + 4x³

Answer 1

The correct formula for the volume of the box, where x is the size of the cut square corners, is V = 11x^2 + 15x^2 - 4x^3, which corresponds to option A.

Step-by-step explanation:

To find the formula that expresses the volume of the box formed by cutting squares from the corners of the sheet and folding up the sides, we need to deduct the side lengths of those squares (each side is x inches long) from the original dimensions of the sheet. The new length and width become (11 - 2x) and (15 - 2x) respectively. The height of the box is equal to the side of the cut square, which is x. Thus, the volume (V) is the product of these dimensions.

The formula for the volume is, therefore:
V = (11 - 2x)(15 - 2x)x = 11x - 2x^2 + 15x - 2x^2 - 4x^3
Simplifying this, we get: V = 11x^2 + 15x^2 - 4x^3

So the correct answer is:
A. V = 11x^2 + 15x^2 - 4x^3