Question

A prism is filled with 48 cubes with a side length of 1/2 unit. What is the volume of the prism in cubic units?

Answer 1

`\boxed{\sf Volume \: of \: prism = 6 \: {units}^(3)}`

Given:

Total numbers of cubes in a prism = 48

Side length of each cube =
`(1)/(2)` unit

Explanation:

`\sf Volume \: of \: cube = {side}^(3) \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {( (1)/(2)) }^(3) \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (1)/(2) * (1)/(2) * (1)/(2) \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (1)/(8) \: { units}^(3)`

`\sf \implies Volume \: of \: prism =Volume \: of \: cube * 48 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (1)/(8) * 48 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{ \cancel{8}} * \cancel{8} * 6 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6 \: {units}^(3)`

Answer 2

6 units cubed

Explanation:

The volume will simply be the volumes of all the little cubes added together.

The volume of a cube is V = s³, where s is the side length. Here, it's 1/2, so:

V = s³ = (1/2)³ = 1/8 units cubed

We have 48 such cubes, so multiply 1/8 by 48 to get the total volume:

48 * (1/8) = 6 units cubed

Thus, the prism is 6 units cubed.

~ an aesthetics lover