Question

3. The formula to find the surface area of a sphere is to take the radius of the sphere and square it and multiply that amount by pi and then multiply that by 4. This is written algebraically as S=4πr 2 , where S is the surface area, r is the radius, and the value of π is 3.14. Rewrite the equation to solve for the radius of the sphere if you know the sphere’s surface area. Then estimate the radius of a sphere given a surface area of 500 meters2 .

Answer 1

The way to get the equation for the radius (r) is to get r by itself. So divide each side by 4pi
500/4pi=r^2
Now take the square root of each side to get the equation of r.
sqrt(500/4pi)=r

Answer 2

Answer:

6.31 m

Step-by-step explanation:

The surface area (S) of a sphere is a function of its radius (r) according to the following expression.

$S=4\pi r^{2}$

We can rewrite it to solve for the radius given the surface area.

$S=4\pi r^{2}\\r^{2} =\frac{S}{4\pi} \\r=\sqrt{\frac{S}{4\pi}}$

When S = 500 m², the radius is

$r=\sqrt{\frac{500m^{2} }{4\pi}}=6.31 m$