Lesson: Challenging Problem Solving - 33t05

Advanced Geometry: Solids

[Page 33 of 37]

Now let's work through the following solids question. Make sure to identify the two critical pieces of information that will lead us on the correct solution path—what we are being asked to find, and what concrete information we are given. Review the following problem and then proceed to the task below.

The dimensions, in centimeters, of rectangular box T are x, y, and z, where x, y, and z are integers. If T has a volume of 22 cubic centimeters, which of the following is the total surface area, in square centimeters, of the two largest faces of T?

	11
	22
	36
	44
	68

Consider your answers to the following questions, and then click Continue.

What is the question asking us to find?
What information has it provided to us?
What shared feature will get us to the correct answer?

Use the information provided by the question stem to find values for x, y, and z. Fill in the boxes below and then click Continue.

x =

y =

z =

Use the information provided by the question stem to find values for x, y, and z. Fill in the boxes below and then click Continue.

Face 1 has an area of square centimeters.

Face 2 has an area of square centimeters.

Face 3 has an area of square centimeters.

Face 1 has a width of 1 and a length of 2 for a total area of 2 square centimeters:
2 1 = 2.
Face 2 has a width of 11 and a length of 2 for a total area of 22 square centimeters: 11 2 = 22.
Face 3 has a width of 11 and a length of 1 for a total area of 11 square centimeters:
11 1 = 11.

The rectangular box is composed of 6 sides (3 pairs of 2 equal sides). This means that there are actually two Face 1's, two Face 2's, and two Face 3's. Face 2 has the largest area, so the surface area of the two largest faces is equal to twice the area of Face 2 – 2 22 = 44. Choice (D) is correct.

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