Question

1. The edge lengths of a right rectangular prism are

Answer 1

Answer:

324 cubes.

Step-by-step explanation:

Let n be the number of cubes with edge length 1/12 meter.

We have been given the lengths of edges of a right rectangular prism as $\frac{1}{2}$ meter, $\frac{1}{2}$ meter and $\frac{3}{4}$ meter.

$\text{Volume of rectangular prism}=L*B*H$, where,

L = Length of prism,

B = Breadth of prism,  

H = Height of prism.

$\text{Volume of cube}=a^3$, where a= length of each edge of the cube.

The volume of n cubes with each edge 1/12 will be equal to the volume of rectangular prism.  

$\text{Volume of n cubes}=\text{Volume of rectangular prism}$

$n\times a^3=L*B*H$

Upon substituting our given values we will get,

$n\times(\frac{1}{12})^3=\frac{1}{2}\times \frac{1}{2}\times \frac{3}{4}$

$n\times\frac{1^3}{12^3}=\frac{1*1*3}{2*2*4}$

$n\times\frac{1}{1728}=\frac{3}{16}$

Let us multiply both sides of our equation by 1728.

$\frac{n}{1728}*1728=\frac{3}{16}*1728$

$n=\frac{3}{16}*1728$

$n=3*108$

$n=324$

Therefore, 324 unit cubes can fit inside the given right rectangular prism.