Answer:
Circumference(C) and surface area(S) of the sphere is given by:
[tex]C = 2 \pi r[/tex]
[tex]S = 4 \pi r^2[/tex]
where, r is the radius of the sphere.
As per the statement:
Circumference(C) = 30 ft
then;
[tex]30 = 2 \pi r[/tex]
Divide both sides by [tex]2 \pi[/tex] we have;
[tex]\frac{15}{\pi} =r[/tex]
or
[tex]r=\frac{15}{\pi}[/tex] ft
We have to find the Surface area of sphere.
Substitute the given values we have;
[tex]S = 4 \pi \cdot (\frac{15}{\pi})^2[/tex]
⇒[tex]S = 4 \pi \cdot \frac{225}{(\pi)^2}[/tex]
⇒[tex]S = 4 \cdot \frac{225}{\pi}[/tex]
Use [tex]\pi=3.14[/tex]
then;
[tex]S = 4 \cdot \frac{225}{3.14}[/tex]
Simplify:
S = 286.624204 square feet
Therefore, the surface area of a sphere is, 286.624204 square feet
