two similar pyramids have volumes 27 and 125. if smaller has

[geo09]

two similar pyramids have volumes 27 and 125. if the smaller has lateral area 18, what is the lateral area of larger?

 

[wjm11]

Re: geometry

Two similar pyramids have volumes 27 and 125. if the smaller has lateral area 18, what is the lateral area of larger?

The ratio of the volumes of similar figures is the cube of the ratio of the linear dimensions. Therefore, the linear dimension ratio is

(Lsmall/Lbig) = (Vsmall/Vbig)^(1/3) = (27/125)^(1/3) = 3/5.

The ratio of the areas of similar figures is the square of the ratio of the linear dimensions. Therefore, the area dimension ratio is

(Lsmall/Lbig)^2 = (Asmall/Abig) = (3/5)^2 = 9/25.

Hope that helps.