Find the volume
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1)
Volume of a container. A cubic shipping container
had a volume of a^3 cubic meters. The height was
decreased by a whole number of meters and the
width was increased by a whole number of meters so
that the volume of the container is now a^3 + 2a^2 - 3a
cubic meters. By how many meters were the height
and width changed?
2)
Decreasing cube. Each of the three dimensions of a
cube with sides of length s centimeters is decreased by a
whole number of centimeters. The new volume in cubic
centimeters is given by
V(s) = s^3 - 13s^2 + 54s - 72.
a) Find V(10).
b) If the new width is s s- 6 centimeters, then what are the
new length and height?
c) Find the volume when s s= 10 by multiplying the
length, width, and height.
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Solution Summary
Find the volume within the problems.
Solution Preview
(1) factor to obtain a(a^2 + 2a - 3) = a(a + 3)(a - 1)
It is now clear that the height was decreased by 1, and ...
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