similar pyramids: find ratios of volumes, bases, areas

[ducksmeowtoo]

two similar pyramids have heights 12 and 18. Find the ratios of the following:
a. base area
b. lateral area
c. total area
d. volumes

 

[jonboy]

Is this a regular pyramid?

 

[skeeter]

linear dimensions will be in the ratio 12/18 = 2/3

areas (all of them) will have the ratio 4/9

volumes will have the ratio 8/27

 

[ducksmeowtoo]

volumes will have the ratio 8/27


^ how does it get to that? :?:

 

[Mrspi]

volumes will have the ratio 8/27


^ how does it get to that? :?:

If two figures are similar, then the ratio of related AREAS is the square of the ratio of any pair of corresponding lengths. If the ratio of the lengths is 2 / 3, then the ratio of areas would be (2 / 3)<SUP>2</SUP>.

If two figures are similar, then the ratio of their VOLUMES is the cube of the ratio of any pair of corresponding lengths. If the ratio the lengths is 2 / 3, then the ratio of the volumes would be (2 / 3)<SUP>3</SUP>.

(2 / 3)<SUP>3</SUP> = (2/3)(2/3)(2/3), or 8/27