Question

F the volume of a spherical droplet is v = \frac{4}{3} \pi r^3v= 3 4 ​ 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.

Answer 1

Given : volume of a spherical droplet is v =  (4/3)πr³  and diameter of Droplet = 2r

To find : write the volume v as a function of the diameter d.

Solution:

v =  (4/3)πr³  

v = volume of Droplet

r = radius of Droplet

Diamter = 2 * radius

=> d = 2r

=> d/2 = r

=>  r = d/2

putting r = d/2 in  (4/3)πr³  

v = (4/3)π(d/2)³  

=> v  =(4/3)π(d³ /8)

=> v = (1/3)π(d³ /2)

=> v = (1/6)πd³

v as a function of the diameter d.  v = (1/6)πd³

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