A postal service says that a rectangular package can have a maximum combined length and girth of 108 inches. The girth of a package is the distance around the perimeter of a face that does not include the length.
a. Identify an inequality that represents the allowable dimensions for the package.
2w+2h≤1082w+2h≤108
2w+2h>1082w+2h>108
2w+2h<1082w+2h<108
2w+2h≥1082w+2h≥108
l+2w+2h≤108l+2w+2h≤108
l+2w+2h≥108l+2w+2h≥108
l+2w+2h<108l+2w+2h<108
l+2w+2h>108
b. Choose three sets of dimensions that are reasonable for the package.
l=12, w=5, h=5l=12, w=5, h=5
l=19, w=35, h=10l=19, w=35, h=10
l=20, w=8, h=12l=20, w=8, h=12
l=30, w=20, h=19
Find the volume of each package.
The first package has a volume
of__in.^3.
The second package has a volume
of__in.^3.
The third package has a volume
of__in.^3.
The fourth package has a volume
of__in.^3.
The first package has a volume of 600 in.^3.
The second package has a volume of 6500 in.^3.
The third package has a volume of 960 in.^3.
The fourth package has a volume of 11400 in.^3.
To find the volume of each package, we need to use the formula for the volume of a rectangular solid:
Volume = length × width × height
a. First, let's calculate the volume of the first package with the dimensions provided: l = 12, w = 5, h = 5.
Volume = 12 × 5 × 5 = 300 cubic inches
So, the volume of the first package is 300 in^3.
b. Next, let's calculate the volume of the second package with the dimensions provided: l = 19, w = 35, h = 10.
Volume = 19 × 35 × 10 = 6650 cubic inches
So, the volume of the second package is 6650 in^3.
c. Finally, let's calculate the volume of the third package with the dimensions provided: l = 20, w = 8, h = 12.
Volume = 20 × 8 × 12 = 1920 cubic inches
So, the volume of the third package is 1920 in^3.
The first package has a volume of (l)(w)(h) = (12)(5)(5) = 300 in.^3.
The second package has a volume of (l)(w)(h) = (19)(35)(10) = 6650 in.^3.
The third package has a volume of (l)(w)(h) = (20)(8)(12) = 1920 in.^3.