Metal to whoever can explain this!
The diameter and height of this cylinder are equal to the side length S of the cube in which the cylinder is inscribed. What is the expression for the cylinders volume?

V=1/4(pi)S^3
V= 1/3 (pi)S^2
V= 1/13(pi)S^3

I know that to find the volume V=(pi)r^2h
I know that the base is equal to the height in the question. I'm thing the first choice is the answer but not really sure even why. Appreciate if someone could explain the process.

Question

Metal to whoever can explain this!
The diameter and height of this cylinder are equal to the side length S of the cube in which the cylinder is inscribed. What is the expression for the cylinders volume?

V=1/4(pi)S^3
V= 1/3 (pi)S^2
V= 1/13(pi)S^3

I know that to find the volume V=(pi)r^2h
I know that the base is equal to the height in the question. I'm thing the first choice is the answer but not really sure even why. Appreciate if someone could explain the process.

anonymous · Answer

Sorry Im still confused. :(
A circle inscribed in a square has a radius HALF OF the square's side

anonymous · Answer

so im basically simplify

anonymous · Answer

No I don't have the answer. I did get this wrong on the test but I doesn't tell you what the correct answer is and need to learn it for the chapter test. :/

cggurumanjunath · Answer

@ash2326

cggurumanjunath · Answer

@agent0smith @bibby @mathmale

cggurumanjunath · Answer

@e.mccormick

cggurumanjunath · Answer

@ikram002p

cggurumanjunath · Answer

@superdavesuper

cggurumanjunath · Answer

@thomaster @texaschic101 @Viveknarayanan @ybarrap

anonymous · Answer

im thinking a  cylinder radius has to be 1/2 to  fit inside a cube
3.14*(1/2)^2 *S*1/4 I may be totally confusing myself here

mathmale · Answer

Your "A circle inscribed in a square has a radius HALF OF the square's side " is really helpful.

If the side length is S, then the radius of the circle is what (in terms of S)?
The height of the cylinder is what (in terms of S)?

The volume of the cylinder is pi (r)^2h, as you have already said.

Substitute your expressions for r and h into that volume formula and you're done.


"im thinking a  cylinder radius has to be 1/2 to  fit inside a cube" would be right if only you'd include "side length S" in this statement.  Please try that.

cggurumanjunath · Answer

@satellite73

ikram002p · Answer

attachment

mathmale · Answer

Beautiful sketch, ikram, and good reasoning.  The only thing I'd do to improve what you've done is to make certain that everything is labeled appropriately and to box in your expression for the volume of the cylinder.  Nice work!

ikram002p · Answer

good , i only did the sketch i sow that u know the volume formula
so thats why i type it 
good luck

anonymous · Answer

V=1/4(pi)S^3 Thanks everyone went over drawing again and iunderstand better. Thanks again!