Question

The circumference C of a sphere is given as 46.1 cm. Find the surface area of the sphere. (Round your answer to two decimal places.)

Answer 1

Sphere's surface
`\approx 676.47\,\,cm^2`

Explanation:

Recall that the circumference of a sphere is related to the sphere's radius (R) via:

`circumference=2\,*\,\pi\,*\,R`

So we can solve for the radius R:

`circumference=2\,*\,\pi\,*\,R\\46.1=2\,\pi\,R\\R=(46.1)/(2\,\pi) \\R=7.337\,\,cm`

Now with this information we can find the surface area of the sphere using the formula:

`Surface= 4\,\pi\,R^2\\Surface=4\,\pi\,(7.337)^2\\Surface\approx 676.47\,\,cm^2`