Question

1. A container company wants to design a cardboard container in the shape of a triangular prism, as shown.

Answer 1

a. Find the surface area of the container. Show your work.
b. Find the volume of the container. Show your work.
c. The company will manufacture the container if the surface area to volume ratio is less than 1. Determine whether the company should manufacture the container. Show and explain your work.

Answer 2

The triangular prism is made up of 5 sides.

We have two congruent triangles, and three rectangles (all of which are different in dimensions). Remember that the area of a triangle is\[A_{\rm triangl e} = {b*h \over 2}\]and for a rectangle\[A_{\rm rectangle} = b*h\]

The surface area is just the sum of all the areas of the sides.

The easiest way to find the volume of the triangular prism is using the triangle side as the "base" and 15 in. side as the "height." The volume equation is\[V = B*h\]where B is the area of the base (the triangle side).

The surface area to volume ratio is simply\[r = {SA \over V}\]