Question

Mia made a right rectangular prism out of cubes with the side length of % inch. What is the volume of the prism in cubic inches? Step 1. Find the number of the small cubes with the fractional edge side to fill the prism (divide the prism edges lengths by the length of the side edge to find out how many cubes fit in) Step 2. Find the volume of one small cube (V = /wh. Barai Step 3. Find the volume of the prism by multiplying volume of one small cube by the number of cubes in the prism. O 105 cubic inches O 13 1/8 cubic inches O 55 cubic inches

Answer 1

We have to calculate the volume of this prism by the method given.

Each little cube have sides of 1/2 of an inch (lets call x to the length to the side of the little cube).

We then will count the multiple of the little cube side the prism has in each dimension.

The prism is 3 sides tall (3x), 5 sides wide (5x) and 7 sides deep (7x).

The volume of the prism is the product of this 3 dimensions, so we can express it as:

`\begin{gathered} V=H\cdot W\cdot L \\ V=3x\cdot5x\cdot7x \\ V=105x^3 \end{gathered}`

As x is the side of the little cube, x^3 is the volume of the little cube.

Knowing that x=0.5 in, we can calculate the volume of the little cube as:

`V_l=x^3=((1)/(2))^3=(1)/(8)in^3`

Then, we can calculate the volume of the prism as:

`V=105x^3=105\cdot V_l=105\cdot(1)/(8)=(104)/(8)+(1)/(8)=13+(1)/(8)`

Answer: The volume of the prism is 13 1/8 cubic inches