The Acme Tennis Ball Company is designing a new box to ship its products. The marketing department wants a triangular box that can hold 4 balls,
as in the illustration below. The balls fit exactly inside the box, just touching all three walls and the end caps of the container.
All 3 walls of the box are the same size.

Assume a tennis ball is 6 cm in diameter, and ignore the thickness of the box material.

Problem 1

The end of the box is in the shape of a triangle.
What is the type and dimensions of the triangle to 2 decimal places?
show answer

An equilateral triangle whose sides are 10.39 cm.

Challenge problem 2

Calculate, to 2 decimal places, the surface area of the box, including the two end caps.
show answer

841.75 cm^{2}

(end caps: 46.765 each, side walls 249.408 each)

(end caps: 46.765 each, side walls 249.408 each)

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