Question

.A candle maker purchased packaging boxes to ship cylindrical candles to customers. The boxes measure 6 in. by 6 in. by 10 in. To keep the candles from damaging, foam inserts with a thickness of 1 2 in. are placed between the candle and the inside of the box on all sides. What is the volume of the largest candle that can be shipped out?
A. 360 in3
B. 282.6 in3
C. 225.6 in3
D. 176.6 in3

Answer 1

If you meant a thickness of 1/2 inch. . .
Because the inserts are put on all the sides, the dimensions of the usable space are 5 X 5 X 9.  This means the diameter of the base is 5.  The radius is half the diameter, so we divide 5 by 2 to get the radius.  5/2 = 2.5.  Now, we plug in the radius and the height (9) into the formula for the volume of a cylinder, which is $volume= \pi r^{2} h$

$v= \pi 2.5^{2} *9=176.6 inches^{3}$

So, D is correct.