Question

Match each set of measures of a and b with the measure of c that gives a volume of 24 cubic inches.

a = 2in and b = 8 in
a = 4in and b = 2 in
a = 3in and b = 4 in
a = 6in and b = 4in

options are
A. c = 2 in
B. c = 3 in
C. c = 4 in
D. c = 6 in

Answer 1

The volume of a triangular base prism is the area of its base times its height.
In this problem, the area of the base is 1/2 (a*c) and the height is b.
So, Volume = 1/2 (a*c)*b or 1/2 (a*b*c). Note that the volume is 24.
If 24 = 1/2 (a*b*c), then 48 = (a*b*c).
Choosing the value of c is reduced to finding a number that when multiplied by a*b gives 48.
On the uploaded chart, look at the first row. a = 2 and b = 8. a*b = 16. So, what times 16 = 48. That is 3 which appears on the row under the "c" column.
Using that strategy, the other values of c can be found without a lot of work.
Last, the matching.