A rectangular container measures 4m by 3 m by 500 cm. The container is completely filled with 0.5 m long cubic packets. How many such packets are needed to fill 3/4 the container?
V = (3/4) * 4 * 3 * (1/2) = 4.5 m^3
v = .5^3 = .125 m^3
4.5 / .125 = ?
If you express the container's dimensions in terms of packets, it is
8x6x1 = 48
3/4 of 48 = 36
To find out how many cubic packets are needed to fill 3/4 of the container, we need to calculate the volume of 3/4 of the container and then divide it by the volume of each cubic packet.
Step 1: Convert measurements to a consistent unit.
The container measures 4m by 3m by 500cm. To ensure the measurements are in the same unit, we need to convert the 500cm to meters.
Since 1m = 100cm, dividing 500cm by 100 gives us:
500cm / 100 = 5m
So the container measures 4m by 3m by 5m.
Step 2: Calculate the volume of the container.
The volume of a rectangular container is calculated by multiplying its length, width, and height. In this case, the volume of the container is:
Volume = Length x Width x Height
Volume = 4m x 3m x 5m
Volume = 60 cubic meters
Step 3: Calculate the volume of 3/4 of the container.
To calculate 3/4 of the container's volume, multiply the container's volume by 3/4:
Volume of 3/4 of the container = (3/4) x 60 cubic meters
Volume of 3/4 of the container = 45 cubic meters
Step 4: Calculate the volume of one cubic packet.
Since the cubic packets are 0.5m long on all sides, the volume of each packet is:
Volume of one cubic packet = 0.5m x 0.5m x 0.5m
Volume of one cubic packet = 0.125 cubic meters
Step 5: Calculate the number of cubic packets needed.
To find the number of cubic packets needed to fill 3/4 of the container, divide the volume of 3/4 of the container by the volume of one cubic packet:
Number of cubic packets needed = (Volume of 3/4 of the container) / (Volume of one cubic packet)
Number of cubic packets needed = 45 cubic meters / 0.125 cubic meters
Number of cubic packets needed = 360 cubic packets
Therefore, 360 cubic packets are needed to fill 3/4 of the container.