160 blocks , each block is 2 cm wide, 1 cm long & 4 cm high, what will be size of box that will hold all 160 blocks (each side cannot be less than 6 cm)
To calculate the size of the box that will hold all 160 blocks, we need to determine the total space required by the blocks.
The width of each block is 2 cm, the length is 1 cm, and the height is 4 cm. Let's calculate the total space required by one block:
Volume of one block = width x length x height
= 2 cm x 1 cm x 4 cm
= 8 cm³
Now, we can calculate the total space required by all 160 blocks:
Total volume = volume of one block x number of blocks
= 8 cm³ x 160
= 1280 cm³
To find the dimensions of the box, we need to consider that each side of the box cannot be less than 6 cm. Therefore, we can calculate the minimum dimensions of the box by dividing the total volume by the minimum side length:
Minimum side length = cube root of (total volume)
= ∛(1280 cm³)
≈ 10.51 cm
Since all sides cannot be less than 6 cm, we can choose the minimum side length and then round it up to the nearest multiple of 6 cm to ensure all sides meet the requirement.
Rounded-up minimum side length ≈ 12 cm
Hence, the size of the box that will hold all 160 blocks is approximately 12 cm x 12 cm x 12 cm.