Question

how many cubic blocks of side length 1/6 inch would take to fill a rectangular prism with a length, width, and height of 1/3 inch, 2/3 inch, and 2/3 inch respectively ?

Answer 1

Volume of one cubic block = (1/6)^3 = 1/216 cu ins

Volume of the prism = 1/3 * 2/3 * 2/3 = 4/27 cu ins

Number of blocks to fill prism = 4/27 / 1/216 = (216*4) / 27 = 32

Answer 2

32

Explanation:

Given:

Side of length cube
`=(1)/(6)\text{ inch}`

Dimension of rectangular prism,

`\text{Length }=(1)/(3)\text{ inch}`

`\text{width }=(2)/(3)\text{ inch}`

`\text{Height }=(2)/(3)\text{ inch}`

Formula:

`\text{Volume of cube }=\text{side}^3`

`\text{Volume of rectangular box }=\text{Length}* \text{Width}* \text{Height}`

Calculation:

Now, we fill rectangular prism with cube block and count number of block.

`\text{Number of block }=\frac{\text{Volume of prism}}{\text{Volume of block}}`

`\text{Number of block }=((1)/(3)* (2)/(3)* (2)/(3))/((1)/(6)* (1)/(6)* (1)/(6))`

`\text{Number of block }=32`

Hence, The number of block to fill rectangular prism is 32