In order to get the surface area of a hemisphere, let's determine its radius first.
Based on the question, the circumference of a great circle is 40.8 inches. Since circumference = 2πr, then 40.8 inches = 2πr. From this, we can solve for the radius.
[tex]40.8=2\pi r[/tex]To solve for the radius, divide both sides of the equation by 2π. Use π = 3.14159
[tex]\frac{40.8}{2\pi}=r[/tex][tex]\frac{40.8}{2(3.14159)}\Rightarrow\frac{40.8}{6.28318}\Rightarrow6.4935[/tex]Therefore, the length of the radius is 6.4935 inches.
Now that we have the radius, let's calculate the surface area of the hemisphere. The formula is:
[tex]SA_{hemisphere}=3\pi r^2[/tex]Let's plug into the formula r = 6.4935 inches and π = 3.14159
[tex]SA_{hemisphere}=3(3.14159)(6.4935in)^2[/tex]Then, solve.
[tex]SA_{hemisphere}=(9.42477)(42.1655in^2)[/tex][tex]SA_{hemisphere}\approx397.4in^2[/tex]Therefore, the surface area of the hemisphere is approximately 397.4 square inches.
