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QUESTION

# The volume of a sphere is given by V = (4/3)πrr3 , where r is the radius. Compute the volume of a sphere with a radius of 199 pm. State your answer in units of m3?

##V = 3.31 * 10^(-29)"m"""^3##

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 = 4/3 * pi * r^3##

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

##V = 4/3 * pi * 7,880,599 * 10^(-36)"m"""^3##

##V = 33,101,176 * 10^(-36)"m"""^3##

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

##V = color(green)(3.31 * 10^(-29)"m"""^3)##

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