Posers and Puzzles
06 Apr 07
06 Apr 07
Originally posted by wittywonkaHexagonal prism:
What is the volume of a right hexagonal prism with each base's perimeter measuring 60 cm and with a height of 5 cm? What about a right octagonal prism with the same measurements?
hexagon side = 10cm.
hexagon area = 6*10*sqrt(3)/4 = 15*sqrt(3) (6 times the area of an equilateral triangle with side length 10)
Volume = base*height = 15*sqrt(3)*5 = 75*sqrt(3).
The octogonal prism can be dealt with in the same way, though the calculations for the area of the base are a little messier.
06 Apr 07
Originally posted by GregMWhy did you divide by four? I think you only divide by two...
Hexagonal prism:
hexagon side = 10cm.
hexagon area = 6*10*sqrt(3)/4 = 15*sqrt(3) (6 times the area of an equilateral triangle with side length 10)
Volume = base*height = 15*sqrt(3)*5 = 75*sqrt(3).
The octogonal prism can be dealt with in the same way, though the calculations for the area of the base are a little messier.
06 Apr 07
No, but I did miss a square: the area of an equilateral triangle with side length S is S^2*sqrt(3)/4, so the correct numbers would be
hexagon area = 6*10^2*sqrt(3)/4 = 150*sqrt(3) (6 times the area of an equilateral triangle with side length 10)
Volume = base*height = 150*sqrt(3)*5 = 750*sqrt(3).
07 Apr 07
1 edit
Originally posted by GregMWhere do you get sqrt(3) from? The area of the triangle is 25*sqrt(2).
No, but I did miss a square: the area of an equilateral triangle with side length S is S^2*sqrt(3)/4, so the correct numbers would be
hexagon area = 6*10^2*sqrt(3)/4 = 150*sqrt(3) (6 times the area of an equilateral triangle with side length 10)
Volume = base*height = 150*sqrt(3)*5 = 750*sqrt(3).
Edit: Posted before checking - I'm thinking of sin(45) 😞