Given:
The circumference of a circle is
[tex]14\pi cm.[/tex]
Required:
We need to find the surface area of a sphere whose circle has a circumference of
[tex]14\pi cm.[/tex]
Explanation:
Consider the circumference of the circle formula.
[tex]C=2\pi r[/tex]
[tex]Substitute\text{ C=}14\pi cm\text{ in the formula.}[/tex][tex]14\pi=2\pi r[/tex][tex]Divide\text{ both sides by }2\pi.[/tex]
[tex]\frac{14\pi}{2\pi}=\frac{2\pi r}{2\pi}[/tex][tex]7=r[/tex]
We get r =7cm.
Consider the surface area of the sphere.
[tex]SA=4\pi r^2[/tex]
Substitute r = in the formula,
[tex]SA=4\pi(7)^2[/tex][tex]SA=4\pi(49)[/tex][tex]SA=196\pi cm^2[/tex]
Final answer:
[tex]The\text{ s}urface\text{ area of the sphere}=196\pi cm^2[/tex][tex]The\text{ s}urface\text{ area of the sphere}=196\times3.14cm^2[/tex][tex]The\text{ s}urface\text{ area of the sphere}=615.44cm^2[/tex]
