One balloon had a volume of 108pi/3 cubic metres.
a.what was the diameter of the balloon?
b.The formula for the volume of a sphere is 4/3(pi)(r^2)
what is the surface area of the balloon?
The formula for volume is[Math] V = \frac{4}{3}\pi r^3[/tex]
So you can just set the volume you have to the volume formula and solve for r, which is the radius. Then the diameter is just twice that.
The formula for the area is $\displaystyle 4 \pi r^2$ so once you have the radius r, just plug it in in this.
Assuming that the balloon is a perfect sphere...
a) The volume of a sphere is
$\displaystyle V = \frac{4}{3}\pi r^3$
Plug in $\displaystyle \frac{108\pi}{3}$ in for V:
$\displaystyle \frac{108\pi}{3} = \frac{4}{3}\pi r^3$
Multiply both sides by $\displaystyle \frac{3}{4\pi}$:
$\displaystyle \begin{aligned}
\frac{108\pi}{3} \cdot \frac{3}{4\pi} &= \frac{4}{3}\pi r^3 \cdot \frac{3}{4\pi} \\
27 &= r^3
\end{aligned}$
Take the cube root of both sides:
$\displaystyle \begin{aligned}
\sqrt[3]{27} &= \sqrt[3]{r^3} \\
r &= 3
\end{aligned}$
The diameter is double the radius, so the answer is 6 meters.
EDIT: too slow! TT_TT