Question

A box in the shape of a rectangular prism is approximately 9 inches long,has an equilateral triangle shaped base with side lengths of 3 inches. The height of the triangular shaped base is 2.5 inches. How many cubic inches of styrofoam peanuts can can be place inside the container?

Answer 1

33.75 cubic inches of styrofoam can be placed inside the container.

Explanation:

Based on given information, the volume of the prism (
`V`), in cubic inches, is determined by using this formula:

`V = (1)/(2)\cdot b\cdot h \cdot l` (1)

Where:

`b` - Base of the triangular face, in inches.

`h` - Height of the triangular face, in inches.

`l` - Length of the prism, in inches.

If we know that
`b = 3\,in`,
`h = 2.5\,in` and
`l = 9\,in`, then the volume of the prism is:

`V = (1)/(2)\cdot b\cdot h \cdot l`

`V = 33.75\,in^(3)`

33.75 cubic inches of styrofoam can be placed inside the container.