Question

The solids are similar. Find the surface area of the red solid.Round your answer to nearest tenth if neceassary.

Answer 1

Step 1:

$\frac{\mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{Sphere}1}{\mathrm{Surface}\mathrm{Area}\mathrm{of}\mathrm{sphere}2}={\left(\frac{\mathrm{Radius}\mathrm{of}\mathrm{Sphere}1}{\mathrm{Radius}\mathrm{of}\mathrm{sphere}2}\right)}^2$

Step 2:

$$\begin{gathered} \frac{5027}{\mathrm{S}}={\left(\frac{20}{15}\right)}^2 \\ \frac{5027}{\mathrm{S}}=\frac{16}{9} \\ \mathrm{S}*16=5027*9 \\ \mathrm{S}=\frac{5027*9}{16} \\ \mathrm{S}=2827.68 \end{gathered}$$

Step 3: So, surface area of red solid is $2728.68{\mathrm{in}}^2$

Final Answer: Surface area of red solid is $2728.68{\mathrm{in}}^2$