A rectangular box is of length 2/5 m. It has a square base of area 9cm*cm. What is the greatest number of 2 cm cubes that can be cut from it?
L = 2/5 = 0.40 m =40m.
V = L*W*h = 40 * 3 * 3 = 360 cm^3.
360cm^3/2cm^3 = 180 Cubes.
Correction: 360cm^3/2^3 = 45 Cubes.
To find the greatest number of 2 cm cubes that can be cut from the rectangular box, we need to determine how many 2 cm cubes can fit into the box.
First, let's convert the length of the box to centimeters. We know that 1 meter is equal to 100 centimeters, so the length of the box in centimeters is (2/5) * 100 = 40 cm.
Next, let's find the volume of the rectangular box. The volume is equal to the area of the base multiplied by the height. Since the base is square and has an area of 9 cm*cm, the length of one side of the base is the square root of 9 cm*cm, which is 3 cm. Therefore, the height of the box is 40 cm / 3 cm = 13.33 cm.
The volume of the box is then length * width * height, which equals 40 cm * 3 cm * 13.33 cm = 1600 cm³.
Now, let's calculate the volume of a single 2 cm cube. The volume of a cube is calculated by multiplying the length of one side by itself three times. For a 2 cm cube, the volume is 2 cm * 2 cm * 2 cm = 8 cm³.
Finally, to find the greatest number of 2 cm cubes that can be cut from the box, we divide the volume of the box by the volume of a single 2 cm cube. Therefore, 1600 cm³ / 8 cm³ = 200.
Therefore, the greatest number of 2 cm cubes that can be cut from the rectangular box is 200.