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

6.31 m

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) =(S)/(4\pi) \\r=\sqrt{(S)/(4\pi)}`

When S = 500 m², the radius is

`r=\sqrt{(500m^(2) )/(4\pi)}=6.31 m`