Question

A box has the shape of a rectangular prism with height 29 cm. If the height is increased

by 0.2 cm, by how much does the surface area of the box increase?
Use pencil and paper. Show your work. Then show a second way to solve the problem.
Explain which way you like better and why.
The surface area increases by
cm²
12 cm
29 cm
7.2 cm

Answer 1

[Method 1] Answer: 7.68 cm²

Explanation:

First, we will solve for the original surface area. We will use the given formula for a rectangular prism's surface area.

SA = 2(wl + hl + hw)

SA = 2((7.2 cm)(12 cm) + (29 cm)(12 cm) + (29 cm)(7.2 cm))

SA = 1,286.4 cm²

Next, we will solve for the new surface area by adding 0.2 cm to 29 cm. We will use the same formula.

SA = 2(wl + hl + hw)

SA = 2((7.2 cm)(12 cm) + (29.2 cm)(12 cm) + (29.2 cm)(7.2 cm))

SA = 1,294.08 cm²

Lastly, we will subtract the old from the new.

1,294.08 cm² - 1,286.4 cm² = 7.68 cm²

[Method 2] Answer: 7.68 cm²

Explanation:

We know that if the height increases by 0.2, this will "add four more boxes" to each side with a height of 0.2. We have two pairs of congruent sides. The area for a rectangle can be found with A = LW.

2 * (0.2 cm * 12 cm) + 2 * (0.2 cm * 7.2 cm)

7.68 cm²