Answer :
Ratio of their volumes = a³ : b³
Ratio of their surface areas =[tex]$\frac{a^{2} + a\sqrt{4h^{2}+a^{2}}}{b^{2} + b\sqrt{4h^{2}+b^{2}}}[/tex]
Step-by-step explanation:
Two square pyramids are similar with their edges are in the ratio of a : b.
Volume of a square pyramid with edge and h = a is given by the formula,
= [tex]$\frac{a^{2}\times h }{3}[/tex] = [tex]$\frac{a^{3} }{3}[/tex]
Volume of a square pyramid with edge b and h = b is given by the formula,
= [tex]$\frac{b^{2}\times h }{3}[/tex] = [tex]$\frac{b^{3} }{3}[/tex]
Ratio of their volumes = a³ : b³ since h/3 gets cancelled.
Total surface area of square pyramid with the edge a =
[tex]$a^{2} + a\sqrt{4h^{2}+a^{2}}[/tex]
Total surface area of square pyramid with the edge b =
[tex]$b^{2} + b\sqrt{4h^{2}+b^{2}}[/tex]
Ratio of the surface area = [tex]$\frac{a^{2} + a\sqrt{4h^{2}+a^{2}}}{b^{2} + b\sqrt{4h^{2}+b^{2}}}[/tex]