Question 219054
A softball is a sphere. The formula for volume of a sphere is:
{{{V = (4/3)pi*r^3}}}
From this formula we can see that in order to find the volume of a sphere all we need to know is "r" (which is the radius).<br>
But we don't know the radius. We do know the circumference however. The formula for circumference is:
{{{C = 2pi*r}}}
So with the circumference, we can find the radius:
{{{27 = 2pi*r}}}
Divide both sides by {{{2pi}}}:
{{{27/(2pi) = r}}}
We can now use this in the volume formula:
{{{V = (4/3)pi*(27/(2pi))^3}}}
To find the exact volume, leave {{{pi}}} in the expression and simplify the expression as much as possible:
{{{V = (4/3)pi*(19683/(8pi^3))}}}
One {{{pi}}} cancels and so does a 4 and a 3 leaving:
{{{V = (6561/(2pi^2))}}} {{{cm^3}}}
which is the exact volume. If you want a decimal approximation of the volume, substitute a decimal approximation of {{{pi}}}. (3.14 is commonly used as a decimal approximation for {{{pi}}}.) A decimal approximation of the V is about {{{332.4}}} {{{cm^3}}}.