Hello, ihmth!

You could have shown us your answer, you know . . .

A set of billiard balls has 15 balls each having a diameter of 2¼ inches.

If the container for the 15 balls will be in the form of a right triangular prism,

find how much cardboard is needed in order to make the container.

I must assume that the balls are in a triangular array, like in the rack,

. . and the box is a triangular "pizza box".

Along the edge of the box (an equilateral triangle), there are five balls.

At each end, there is this arrangement: Code:

\
\
* * * \
* *\
* *
* *
\
* C *\
* * * \
* : * \
: \
* : * \
* : * \
* : * 60° \
- - - - - * * * - - - - - - - *
A B

The radius is:

. . And we find that: .

Make a sketch of the five balls in a row and the edges of the box.

The length of the edge is: .

. . Hence: .

The top and bottom of the box are equilateral triangles of side

The area of an equilateral triangle of side is: .

The sides of the box are three rectangles of dimensions: .

I'll let you crank out the arithmetic . . .