Question

PLEASE HELP! WILL VOTE AND BRAINLIEST!
1.How is the volume formula derived for each of the following:
a)cylinder
b)pyramid
c)cone
2.How do changes in the dimensions of a cube change its volume? If the side length was doubled how would the volume change?
3.What are the two-dimensional cross-sections (parallel, perpendicular, and diagonal to the base) for the following:
a)cylinder
b)cone
c)sphere
d)square pyramid
4.How are the cross-sections in #3 related to Cavalieri's Principal?

Answer 1

1. 
a)cylinder: V = π r² h
b)pyramid: 1/3 · [area of base] · h
c)cone: (1/3)πr²h


2.
The changes in the dimensions of a cube changes its volume by 8 This essentially means that the original side length and volume is 1 cubic unit. However, when you double the side then the volume will finally be 8 cubic units. Therefore, the volume multiplies by eight.

3.
a)cylinder - Ellipse
b)cone - Circle
c)sphere - Great Circle 
d)square pyramid - Triangle