Question

How many cubic blocks of side length 1/7 would it take to fill a rectangular prism with a length, width, and height of 3/7 inch, 1/7 inch, and 3/7 inch, respectively

Answer 1

Answer:

441 number of cubic blocks will fill the rectangular prism.

Step-by-step explanation:

Volume of rectangular prism is,

$V_{Prism}=\text{Length}\times\text{Width}\times\text{Height}$

Putting all the values,

$V_{Prism}=\dfrac{3}{7}\times\dfrac{1}{7}\times\dfrac{3}{7}$

$=\dfrac{3\times1\times3}{7}$

$=\dfrac{9}{7}\ in^3$

Volume of cubic block is,

$V_{Cube}=\text{Side}^3$

Putting all value,

$V_{Cube}=\left(\dfrac{1}{7}\right)^3=\dfrac{1}{343}\ in^3$

Number of cubic blocks that can fill the rectangular prism is,

$=\dfrac{V_{Prism}}{V_{Cube}}=\dfrac{\frac{9}{7}}{\frac{1}{343}}=\dfrac{9\times 343}{7\times 1}=441$