Question 61384
The surface of a sphere is 86 pie ft^2? what is the diameter of the sphere?
The formula for the surface area of a sphere is {{{highlight(S=4*pi*r^2)}}}
{{{S=86*pi}}} ft^2
{{{86*pi=4*pi*r^2}}}
{{{86*pi/(4*pi)=4*pi*r^2/(4*pi)}}}
{{{21.5=r^2}}}
{{{sqrt(21.5)=sqrt(r^2)}}}
{{{4.636809248=r}}}
Diameter = 2*radius
{{{d=2(4.6268091248)}}}
d=9.2736 ft
:
You can substitute r=d/2 into the formula and reduce your formula:
{{{S=4*pi*(d/2)^2}}}
{{{S=4*pi*(d^2/4)}}}
{{{S=4*pi*d^2/4}}}
{{{S=pi*d^2}}}
 substitute {{{S=86*pi}}} into the formula and solve for d.
{{{86*pi=pi*d^2}}}
{{{86*pi/(pi)=pi*d^2/(pi)}}}
{{{86=d^2}}}
{{{sqrt(86)=sqrt(d^2)}}}
{{{sqrt(86)=d}}}
{{{d=sqrt(86)}}}ft
That's as pretty as I can make it.  If you put that in your calculator, you'll see it's the same answer.
Happy Calculating