1/// The truck for a moving company has interior dimensions of 187" x 89" x 77" but dimensions of the storage boxes are 24" x 14" x 27"
if the moving company needs to move 200 storage different determine how many trucks will be needed
2/// Gomer stores his iguana food in a van that is 8 inches tall and has a diameter of 6 inches He stores his hamster food in a can that is 10 inches tall and has a diameter of 5 inches which can is larger.
a) the iguana food can
b) the hamster food can
c) they are the same size
d) insufficient amount of information to know
2. Iguana food:
V = pi*r^2*h = 3.14 * 3^2 * 8 = 226.1 in^3.
Hamster food:
V = 3.14 * 2.5^2 * 10 = 196.3 in^3.
1. Vt = 187*89*77 = 1,281,511 in^3 per truck.
Vb = 24*14*27 = 9,072 in^3 per box.
9,072in^3/box * 200boxes = 1,814,400 in^3 of space needed.
1,281.511*N = 1,814,400.
N = 1,814,400/1,281,511 = 1.4 or 2 trucks.
1) To determine how many trucks will be needed to move 200 storage boxes, we need to calculate the total volume of the storage boxes and then divide it by the volume of the truck's interior.
Volume of each storage box = length x width x height = 24" x 14" x 27" = 9,072 cubic inches
Total volume of 200 storage boxes = 9,072 cubic inches/box x 200 boxes = 1,814,400 cubic inches
Volume of the truck's interior = length x width x height = 187" x 89" x 77" = 1,207,623 cubic inches
Number of trucks needed = Total volume of storage boxes / Volume of truck's interior = 1,814,400 cubic inches / 1,207,623 cubic inches ≈ 1.50 trucks
Since we cannot have a fraction of a truck, we would need to round up to the nearest whole number. Therefore, we would need 2 trucks to move 200 storage boxes.
2) To determine which can is larger, we can compare their volumes.
Volume of the iguana food can = π x (diameter/2)^2 x height = π x (6 inches/2)^2 x 8 inches
≈ 18.85 cubic inches x 8 inches ≈ 150.8 cubic inches
Volume of the hamster food can = π x (diameter/2)^2 x height = π x (5 inches/2)^2 x 10 inches
≈ 12.27 cubic inches x 10 inches ≈ 122.7 cubic inches
Since 150.8 cubic inches is greater than 122.7 cubic inches, the iguana food can is larger than the hamster food can. Therefore, the answer is a) the iguana food can.
1/// To determine how many trucks will be needed to move 200 storage boxes, we need to calculate the total volume of the boxes and compare it to the available volume in each truck.
First, let's calculate the volume of one storage box:
Volume = length x width x height
Volume = 24" x 14" x 27" = 9,072 cubic inches
Next, let's calculate the total volume of all 200 storage boxes:
Total volume of boxes = volume of one box x quantity of boxes
Total volume of boxes = 9,072 cubic inches x 200 = 1,814,400 cubic inches
Now, let's calculate the available volume in each truck:
Available volume in truck = interior length x interior width x interior height
Available volume in truck = 187" x 89" x 77" = 1,247,103 cubic inches
Finally, let's calculate the number of trucks needed:
Number of trucks = Total volume of boxes / Available volume in truck
Number of trucks = 1,814,400 cubic inches / 1,247,103 cubic inches
Number of trucks ≈ 1.457 (rounded up to the nearest whole number)
Therefore, the moving company will need 2 trucks to move 200 storage boxes.
2/// To determine which can is larger, we need to compare their volumes.
Let's calculate the volume of the iguana food can:
Volume = π x (radius)^2 x height
Radius = diameter / 2 = 6 inches / 2 = 3 inches
Volume = π x 3^2 x 8 inches
Volume ≈ 226.195 cubic inches (rounded to three decimal places)
Next, let's calculate the volume of the hamster food can:
Volume = π x (radius)^2 x height
Radius = diameter / 2 = 5 inches / 2 = 2.5 inches
Volume = π x 2.5^2 x 10 inches
Volume ≈ 196.349 cubic inches (rounded to three decimal places)
Therefore, the iguana food can has a larger volume than the hamster food can.
Answer: a) the iguana food can