If the volume of a spherical droplet is 𝑉=43𝜋𝑟3V= 34 πr 3 and the diameter of the droplet is twice the radius, 𝑑=2𝑟d=2r, write the volume V as a function of the diameter d.
Question
If the volume of a spherical droplet is 𝑉=43𝜋𝑟3V= 34 πr 3 and the diameter of the droplet is twice the radius, 𝑑=2𝑟d=2r, write the volume V as a function of the diameter d.
Solution
The volume of a sphere is given by V = 4/3 * π * r^3.
We are given that the diameter d = 2r.
We can express r in terms of d by rearranging the equation to get r = d/2.
Substitute r = d/2 into the volume equation to get V = 4/3 * π * (d/2)^3.
Simplify the equation to get V = 1/6 * π * d^3.
So, the volume V of the sphere as a function of the diameter d is V = 1/6 * π * d^3.
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