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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?
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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?
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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. |
The volume of a rectangular box is equivalent
to the product of the 3 edge lengths. Therefore, our first step is to
determine the prime factors of 22 to determine possible edge lengths.
The question stem states that the edges are all integers, so we don't
need to worry about fractions as edge lengths:
22 = 2 
11
According to our factorization, the product 22
is composed of exactly 2 prime factors; we cannot factor 22 any further.
However, the rectangular box has 3 edges, not 2. In order to maintain
a volume of 22 cubic centimeters, the third edge must measure 1 centimeter.
Therefore, 11, 2, and 1 must be the lengths of the longest, middle, and
shortest edges of the box.
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Video Lessons and 10 Fully Explained Grand Tests
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