Proof of parallelism and verticality in solid geometry 22

(1). certificate: because ABB 1A is the shaft section = = & gtAB is the diameter = = & gtBC⊥AC.

ABB 1A is the shaft section = = >; A 1A is bus = =>A 1A⊥ surface ACB== >A 1A⊥BC.

= = & gtBC⊥ airplane A 1AC== >

Face A 1BC⊥ Face A 1AC

Using the decision theorem: if one plane passes through the vertical line of another plane, then the two planes are perpendicular to each other.

(2).

Assuming that the radius of the bottom surface of the cylinder is r and the height is h, the volume of the cylinder is V 1=.

πr^2h.

With the proof of 1, we can see that

A 1C 1⊥ is b 1c 1 and a1⊥ bb1is a1c/. So the height of pyramid A 1-BCC 1B 1 c1= ab/√ 2 = √ 2 * r, and the area of bottom BCC 1B 1 is.

*√2*rh*√2*r=2/3

*r^2h

Volume ratio of quadrangular pyramid to cylinder

V2

/

V 1

=

2

/

(3π)