2007-06-12 05:56:54 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Hi,
The volume is 216 cm³
To find the length of a diagonal of a rectangular prism, use the formula distance = √(x² + y² + z²). Since this prism is a cube all 3 sides are the same, so distance = √(x² + x² + x²). This simplifies to distance = √(3x²). This radical simplifies to:
......................._
distance = x√3
In this case 6√3 = x√3 would solve that x = 6. If each side is 6 then volume = s³. 6³ = 216, so the volume is 216 cm³.
I hope that helps!! :-)
2007-06-12 06:02:01 · answer #1 · answered by Pi R Squared 7 · 1⤊ 0⤋
The diagonal of a cube is Side(Sqrt3).
You can prove that by algebra, but just follow allow the formula and trust it
The side of the cube is 6.
The volume of the cube would be 6*6*6=6^3
216cm^3=volume
2007-06-12 06:02:11 · answer #2 · answered by UnknownD 6 · 1⤊ 0⤋
A face diagonal = rad2 x where x is the side length.
The cube diagonal is rad3 x.
rad3 x = 6 rad3
x = 6
volume is 6^3 = 216
2007-06-12 06:03:45 · answer #3 · answered by gebobs 6 · 0⤊ 0⤋
3l^2=108
l^2=36
l=6cm is each side
volume of cube=6^3=216cm^3
2007-06-12 06:02:41 · answer #4 · answered by Anonymous · 0⤊ 0⤋
do your own homework!
you won't learm anything unless you do
2007-06-12 06:06:25 · answer #5 · answered by ray d 4 · 0⤊ 0⤋