Question

Josie has 250 cubic centimeters of candle wax. She wants to make a hexagonal prism candle with a base area of 21 square centimeters and a height of 8 centimeters. She also wants to make a triangular prism candle with a height of 14 centimeters. Can the base area of the triangular prism candle be 7 square centimeters?

Answer 1

Let's compute the volume of the hexagonal prism candle. That volume is

Volume = (area of base)*(height)
Volume = 21*8
Volume = 168

The volume of the hexagonal prism candle is 168 cubic cm

So we have 250-168 = 82 cubic centimeters of wax leftover. 

Let V = 82 be the volume of the triangular prism. We're given the height to be 14 so h = 14

Use V = 82 and h = 14 to find the area of the base (A)

V = A*h
82 = A*14
82/14 = A*14/14
A = 5.857 ... this is approximate

The base area is about 5.857 square cm which is less than 7 square cm. So it's impossible for the base area to be 7 square cm. The area of the base must be 5.857 (approx) or smaller if we want the height to be 14 cm. 

The answer to the question in the problem is simply "no" with the reasoning explained above.