Yet Another Geometry Problem

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?

Originally posted by wittywonka
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?

I could do this, but I suspect it's your homework.

Originally posted by AThousandYoung
I could do this, but I suspect it's your homework.

Lol...I can do it too. Actually, it was my homework, but it was several chapters ago.

Here, to prove it, the formula is V=((P*a)/2)*(H)

The only problem is knowing what those variables mean... 😛

Originally posted by wittywonka
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?

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.

Originally posted by GregM
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.

Why did you divide by four? I think you only divide by two...

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).

Originally posted by GregM
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).

Where do you get sqrt(3) from? The area of the triangle is 25*sqrt(2).

Edit: Posted before checking - I'm thinking of sin(45) 😞