Question

Pyramid a and pyramid b have surface areas 135cm and 60cm respectively. the volume of pyramid a is 405cm. work out the volume pyramid B

Answer 1

Check the picture below.

`\cfrac{s^2}{s^2}~~ = ~~\stackrel{Areas}{\cfrac{135}{60}}\implies \cfrac{s^2}{s^2}~~ = ~~\cfrac{9}{4}\implies \left( \cfrac{s}{s} \right)^2=\cfrac{9}{4}\implies \cfrac{s}{s}=\sqrt{\cfrac{9}{4}}\implies \cfrac{s}{s}=\cfrac{3}{2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{s^3}{s^3}~~ = ~~\stackrel{Volumes}{\cfrac{405}{V}}\implies \cfrac{(3)^3}{(2)^3}=\cfrac{405}{V}\implies \cfrac{27}{8}=\cfrac{405}{V} \\\\\\ 27V=3240\implies V=\cfrac{3240}{27}\implies {\LARGE \begin{array}{llll} V=120 \end{array}}`