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The volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure. VA = 27m3 and VB = 64m3 and SA = 63m2

Sagot :

,For similar figures we have:

[tex]\begin{gathered} (q)^3=\frac{V_b}{V_a} \\ (q)^2=\frac{S_b}{S_a} \end{gathered}[/tex]

where q stands for the scale factor, V for the volume and S for the area.

Now, because we have both volumes, we calculate q as follows:

[tex]\begin{gathered} q^3=\frac{64}{27} \\ q=\sqrt[3]{\frac{64}{27}} \\ q=\frac{4}{3} \end{gathered}[/tex]

Now, we use the value found for q and the given value of Sa to find the value of Sb, as follows:

[tex]\begin{gathered} (\frac{4}{3})^2=\frac{S_b}{63} \\ S_b=\frac{63\cdot16}{9} \\ \\ S_b=112m^{2} \end{gathered}[/tex]

From the solution developed above, we are able to conclude that the solution is Sb = 112 m²

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