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Find how much cardboard is needed in order to make the container?
A set of billiard ball contains 15 numbered balls each having a diameter of 2.25 inches. If the container for the 15 billiard balls will be in the form of a right triangular prism, find how much cardboard is needed in order to make the container?
Kindly show complete solution... thanks
Supposing the arrangement to be triangles of 3 balls stacked 5 high, the container will consist of 3 side pieces in the shape of rectangles and 2 end pieces in the shape of equilateral triangles. Using the first source below which gives a ratio of 1:5.464 between the radius of the spheres and side of the enclosing triangle, we can calculate the triangle side to be:
(2.25 / 2) x 5.464 = 6.147 inches
so each of the 3 rectangular sides of the container needs to be 6.147 inches wide and 5 x 2.25 = 11.25 inches tall. So each rectangular side has area 69.15 square inches, and all three have area 207.5 square inches.
Using the second source below, the area of each of the triangular ends is ((sqrt(3)) / 4) x 6.147^2 = 16.36 square inches
and both ends together have area 32.7 square inches
And the total amount of cardboard (neglecting the thickness of the cardboard) required is 240.2 square inches.
Pool Lessons & Billiard Instruction - Set & Slow Back Stroke