a company sells snack-size boxes of raisins with dimensions 5 in. by 2.5 in. by 1.5 in., each weighing 2 oz. They want to make a family-size box that would be 7.5 in. by 3.75 in. by 2.25 in. What would be the weight of the family-size box of raisins?
5 * 2.5 * 1.5 = 18.75 cubic in = 2 oz.
7.5 * 3.75 * 2.25 = 63.28 cubic in
2 (63.28 /18.75) = 6.75 oz. family size
Thank you
To calculate the weight of the family-size box of raisins, we need to use the concept of density. The density of an object is defined as its mass (weight in this case) divided by its volume.
First, let's find the volume of the snack-size box of raisins and the family-size box of raisins.
The volume of a box can be calculated by multiplying its length, width, and height.
For the snack-size box, the volume would be:
Volume_snack = length_snack × width_snack × height_snack
= 5 in. × 2.5 in. × 1.5 in.
For the family-size box, the volume would be:
Volume_family = length_family × width_family × height_family
= 7.5 in. × 3.75 in. × 2.25 in.
Next, we need to find the weight (mass) of the snack-size box. It is given as 2 oz.
Now, we can set up a proportion to find the weight of the family-size box.
Since density is mass divided by volume, we have:
Density_snack = Weight_snack / Volume_snack
Using this, we can calculate the density of the snack-size box.
Density_snack = 2 oz / (5 in. × 2.5 in. × 1.5 in.)
Now, we can use the density of the snack-size box to calculate the weight of the family-size box.
Weight_family = Density_snack × Volume_family
Plugging in the values, we have:
Weight_family = (2 oz / (5 in. × 2.5 in. × 1.5 in.)) × (7.5 in. × 3.75 in. × 2.25 in.)
Simplifying this expression will give us the weight of the family-size box of raisins.