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.)

Question

asked Jan 25, 2021 99.0k views

1 Answer

Eilleen · Answer 1 · 2021-01-31T05:29:33+0000

Answer:

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:

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