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Jacinta compares the volume of two boxes. Both boxes have a width of 2.5 inches, and a height of 10 inches. The
larger box has a length of 8 inches. The smaller box has a length that is 75% of the length of the larger box.
(a)
Volume of large box =
<
(b) Volume of small box =
(c) What is the difference in the volumes of the two boxes?
(d)
Which units should be used for each of these answers?

User Mswanberg
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1 Answer

6 votes

Explanation:

w(idth) = 2.5 inches for both boxes

h(eight) = 10 inches for both boxes

l(ength)l(arge) = 8 inches

l(ength)s(mall) = 75% of ll (=> of 8 inches)

=> ls = 8 × 75/100 = 2 × 75/25 = 2 × 3 = 6 inches

vl (volume large) = 8 × 2.5 × 10 = 200 inches³

vs (volume small) = 6 × 2.5 × 10 = 150 inches³

the difference of these two volumes is 50 inches³

the units to be used is cubic inches (inches³). we are talking about volumes. not lengths (inches), not areas (inches²).

the reason - for a volume we need to multiply 3 lengths (measured in simple inches). so, inch multiplied by inch is inch². this multiplied by inch again is then inch³.

User Yonatan Naor
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