# Question 6e9f3

Aug 30, 2015

$V = 3.31 \cdot {10}^{- 29} {\text{m}}^{3}$

#### Explanation:

All you really need to do here is plug the value of $r$ in the formula for the volume of the sphere and solve for $V$.

Before doing that, convert the radius from picometers to meters

199color(red)(cancel(color(black)("pm"))) * "1 m"/(10^12color(red)(cancel(color(black)("pm")))) = 199 * 10^(-12)"m"

The volume of the sphere - expressed in cubic meters - will be

$V = \frac{4}{3} \cdot \pi \cdot {r}^{3}$

V = 4/3 * pi * (199 * 10^(-12)"m")""^3#

$V = \frac{4}{3} \cdot \pi \cdot 7 , 880 , 599 \cdot {10}^{- 36} {\text{m}}^{3}$

$V = 33 , 101 , 176 \cdot {10}^{- 36} {\text{m}}^{3}$

Round this off to three sig figs, the number of sig figs you gave for the radius of the sphere, to get

$V = \textcolor{g r e e n}{3.31 \cdot {10}^{- 29} {\text{m}}^{3}}$