Question

what is the surface area of a sphere with a 16cm circumference

Answer 1

Let's start with the basic equations first:\[C=\pi(2r)=\pi(D)\] and \[SA = \pi(4r ^{2})\] where r, D, and SA are the radius, diameter, and SA is the surface area of the sphere.

Let's first find r by substituting what we know into the equation for circumference:\[16cm=\pi(2r)\]Now solve for r:\[r=\frac{ 16 }{ 2\pi }=\frac{8}{\pi}\]I'm keeping it in terms of pi for simplicity.

Use the value for r and substitute into the equation for SA:\[SA=4\pi \left(\frac{8}{\pi}\right)^2=4\pi \frac{ 64 }{ \pi^2 }=\frac{ 256 }{ \pi }\]Now, we just divide 256 by pi and get 81.5cm. Hope this helps! Welcome to Open Study!