Mathematics: Two square pyramids are similar. If the ratio of a pair of corresponding edges is a : b, what is the ratio of their volumes? What is the ratio of their surface areas?

The angle is 105 degrees. This angle along with the 75 degree angle make a straight line , 180-75 = 105 degrees...

Two square pyramids are similar. If the ratio

Maxwell8066

22.01.2022

Ratio of their volumes = a³ : b³

Ratio of their surface areas = $$\frac{a^{2} + a\sqrt{4h^{2}+a^{2}}}{b^{2} + b\sqrt{4h^{2}+b^{2}}}$

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,

= $$\frac{a^{2}\times h }{3}$ = $$\frac{a^{3} }{3}$

Volume of a square pyramid with edge b and h = b is given by the formula,

= $$\frac{b^{2}\times h }{3}$ = $$\frac{b^{3} }{3}$

Ratio of their volumes = a³ : b³ since h/3 gets cancelled.

Total surface area of square pyramid with the edge a =

$$a^{2} + a\sqrt{4h^{2}+a^{2}}$

Total surface area of square pyramid with the edge b =

$$b^{2} + b\sqrt{4h^{2}+b^{2}}$

Ratio of the surface area = $$\frac{a^{2} + a\sqrt{4h^{2}+a^{2}}}{b^{2} + b\sqrt{4h^{2}+b^{2}}}$

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