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

Answer:

32

Step-by-step explanation:

Given:

Side of length cube $=\frac{1}{6}\text{ inch}$

Dimension of rectangular prism,

$\text{Length }=\frac{1}{3}\text{ inch}$

$\text{width }=\frac{2}{3}\text{ inch}$

$\text{Height }=\frac{2}{3}\text{ inch}$

Formula:

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

$\text{Volume of rectangular box }=\text{Length}\times \text{Width}\times \text{Height}$

Calculation:

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

$\text{Number of block }=\dfrac{\text{Volume of prism}}{\text{Volume of block}}$

$\text{Number of block }=\dfrac{\frac{1}{3}\times \frac{2}{3}\times \frac{2}{3}}{\frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}}$

$\text{Number of block }=32$

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

Answer 2

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