The volume of a sphere is given by V=(4/3)3.14r^3, where r is the radius. Compute the volume of a sphere with a radius of 329pm. state your answer in units of m^3.
r=329pm=329E-12 m
r^3= (3.29E-10)^3=35.6E-30m^3
Put that in the formula, and compute V
To compute the volume of a sphere with a given radius of 329 pm, we need to plug the value of the radius into the formula for the volume of a sphere.
First, let's convert the radius from picometers (pm) to meters (m). Since 1 m = 10^12 pm, we can calculate the radius in meters as follows:
329 pm * (1 m / 10^12 pm) = 329 * 10^(-12) m = 3.29 * 10^(-10) m
Now we can substitute this value of the radius into the formula for the volume of a sphere, which is given by:
V = (4/3) * π * r^3
V = (4/3) * π * (3.29 * 10^(-10))^3
Now let's simplify the expression and calculate the volume:
V = (4/3) * 3.14 * (3.29 * 10^(-10))^3
V = (4/3) * 3.14 * (3.29)^3 * (10^(-10))^3
V = (4/3) * 3.14 * 3.29^3 * 10^(-30)
V ≈ 1.59 * 10^(-29) m^3
Therefore, the volume of the sphere with a radius of 329 pm is approximately 1.59 * 10^(-29) m^3.