A block of wood is in the form of a cube whose edge is 7 m. How many small rectangular blocks of size 25 cm*8 cm*5 cm* can be cut from the block, if there is no wastage of wood?
7m = 7000cm
7000/25 = 280
7000/8 = 875
7000/5 = 1400
SO, there are 280*875*1400 = 343000000 blocks
To find the number of small rectangular blocks that can be cut from the larger cube without any wastage of wood, we need to determine how many times the dimensions of the small block can fit into the dimensions of the larger cube.
Given:
- The edge length of the larger cube is 7 m.
- The dimensions of the smaller block are 25 cm, 8 cm, and 5 cm.
First, let's convert the dimensions to the same unit. Since the edge length of the larger cube is given in meters, we'll convert the dimensions of the smaller block to meters as well.
1 meter = 100 centimeters, so:
- The length of the smaller block is 25 cm = 25/100 m = 0.25 m.
- The width of the smaller block is 8 cm = 8/100 m = 0.08 m.
- The height of the smaller block is 5 cm = 5/100 m = 0.05 m.
Now, we can find the number of small rectangular blocks that can fit within the larger cube.
Since the larger cube has dimensions of 7 m * 7 m * 7 m, and the smaller block has dimensions of 0.25 m * 0.08 m * 0.05 m, we can calculate the number of replicates in each dimension:
Number of replicates along the length = 7 m / 0.25 m = 28.
Number of replicates along the width = 7 m / 0.08 m = 87.5 (rounded down to 87).
Number of replicates along the height = 7 m / 0.05 m = 140.
To find the total number of blocks, we multiply these three values together:
Total number of blocks = 28 * 87 * 140 = 340,320.
Therefore, you can cut 340,320 small rectangular blocks of size 25 cm * 8 cm * 5 cm from the larger cube without any wastage of wood.