Question

two similar pyramids have heights 9 and 12, Find the ratios of the base areas, lateral areas, total areas, and volumes.

Answer 1

Ratio of the total surface area = Ratio of the lateral areas = ratio of the base area = 9 : 16

Ratio of the volumes = 27 : 64

Explanation:

Two similar pyramids have the heights 9 units and 12 units respectively.

Ratio of their heights are =
`(9)/(12)` =
`(3)/(4)`

By the property of similar figures,

"If the two figures are similar, their corresponding sides will be proportional".

Therefore, all the dimensions of these similar pyramids will be in the same ratio.

Therefore, ratio of their total surface areas = ratio of lateral areas = ratio of the base area =
`((3)/(4))^2` =
`(9)/(16)`

Similarly, ratio of their volumes =
`((3)/(4))^3` =
`(27)/(64)`