Question

A box has the shape of a rectangular prism with height 30 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.
13 cm
30 cm
8.7 cm

Answer 1

8.68 cm²

Explanation:

You want the increase in surface area of a box with length and width 13 cm and 8.7 cm when the height is increased from 30 cm by 0.2 cm.

Area

The increase in area is effectively the lateral area of the prism whose length and width are the same, but whose height is 0.2 cm. That is ...

A = Ph = 2(L+W)h

A = 2(13 cm +8.7 cm)(0.2 cm) = 8.68 cm²

The surface area increases by 8.68 cm².

Alternate solution

We can find the total area of the box with the different dimensions, then subtract the original area from the increased area.

A = 2(LW +H(L+W))

A1 = 2(13·8.7 +30(13 +8.7)) = 1528.2 cm²

A2 = 2(13·8.7 +30.2(13 +8.7)) = 1536.88 cm²

The increase in area is 1536.88 -1528.2 = 8.68 cm².

We prefer the first solution, as it requires a lot less arithmetic.

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