91Ó°ÊÓ

Volume is defined as the amount of space that a particular object or body occupies in the space.

The radius of the spherical beach ball, $r=0.84Â\pm 0.04\mathrm{m}$.

The formula of the volume of a sphere is

$V=\frac{4}{3}\mathrm{π}{r}^3…\left(i\right)$

From equation (i), the volume is

$V=\frac{4}{3}\mathrm{Ï€}{\left(0.84\right)}^3$.

Thus, the final value of the multiplication is0.6%.

Differentiating equation (i) w.r.t to radius,

$\frac{\mathrm{d}V}{\mathrm{d}r}=\frac{4}{3}\mathrm{Ï€}3r^2\mathrm{d}r$.

The formula of the small change in the volume of a sphere is

role="math" localid="1643623569468" $\mathrm{d}V=4\mathrm{π}{r}^2\mathrm{d}r…\left(ii\right)$.

From equation (ii), the small change in the volume is

$\mathrm{d}V=4\mathrm{Ï€}{\left(0.84\right)}^2\left(0.04\right)$.

The formula of percent uncertainty is

$V\text{'}=\frac{\mathrm{d}V}{V}×100\%…\left(iii\right)$.

From equation (iii), the value of percent uncertainty is

$\begin{array}{c}V\text{'}=\frac{4\mathrm{π}{\left(0.84\right)}^2\left(0.04\right)}{\frac{4}{3}\mathrm{π}{\left(0.84\right)}^3}×100\%\\ ≈10\%\end{array}$

Thus, the final value is 10%.