BSubtract the volume of the candle from the volume of the bag.
CStart by finding the volume of package material needed to fill the empty space in 70 bags.
AVolume of the Bag: 132 cubic inches Volume of the Candle: about 29.5 cubic inches
Babout 102.5 cubic inches
C13 packages
Practice makes perfect
We are asked to find the volume of the bag and candle. We will do this one at a time. Let's start with the bag. We know that the bag is 5.5in.* 3in. * 8in. Using the fact that the bag is a rectangular prism, we can draw it.
Recall that the volume of a rectangular prism with length l, width w, and height h can be calculated using the following formula.
V=l w hWe are given that l= 3, w= 5.5, and h= 8, so we have enough information to calculate the volume of the rectangular prism.
The volume of the bag is 132 cubic inches. Next, we will calculate the volume of the candle. We know that the candle is 6in. tall and 2.5in. across. Using the fact that the candle is a cylinder, we can draw it.
Recall that the volume of a cylinder with the radius r and height h can be calculated by the following formula.
V=Ï€ r^2 h
In this case, we are given the diameter and the height of the cylinder. To find the radius we can divide the diameter d by 2.
We got that the radius of the candle is 1.25 inches. Now, we can substitute the height and the radius into the formula and calculate the volume of the candle.
The volume of the candle is about 29.5 cubic inches.
We want to find the volume of the empty space in the bag after the candle is placed in the bag. To do so, we need to subtract the volume of the candle from the volume of the bag. In Part A, we got that the volume of the bag is 132 cubic inches and the volume of the candle is about 29.5 cubic inches. Let's subtract these volumes.
132-29.5=102.5
Therefore, we need about 102.5 cubic inches of packing material to fill the empty space in the bag after the candle is placed in the bag.
We are asked to find how many packages of packing material is needed to fill 70 gift bags. From Part B, we know that we need about 102.5 cubic inches of packing material to fill the empty space in one bag. Let's calculate the volume of packing material needed to fill the empty space in 70 bags.
102.5* 70 = 7175
We got that we need about 7175 cubic inches of packing material to fill the empty space in 70 bags. Knowing that each package of packing material contains 575 cubic inches of material, we can get the number of packages of material needed to fill the empty space in 70 bags.
7175/575=12.478...
Note that the number of packages has to be an integer. Therefore, 13 packages of material is needed to fill all of the gift bags.
