The problem reads as follows: You are told that the volume of a sphere isV=4r3/4, where V is the volume and d is thediameter of the sphere. Is this equation dimensionallycorrect? (Use SI unity analysis to find out) note: I am a new to Physics and would like to know ifsomeone can help me understand the whole thought behind thisquestion. Thank you. The problem reads as follows: You are told that the volume of a sphere isV=4r3/4, where V is the volume and d is thediameter of the sphere. Is this equation dimensionallycorrect? (Use SI unity analysis to find out) note: I am a new to Physics and would like to know ifsomeone can help me understand the whole thought behind thisquestion. Thank you.
Explanation / Answer
Volume of the sphere is V = (4/3)r3 it's not V= 4r3/4 As we know that Density () = m/V Then the volume is V = m/ = kg/kg/m3 =m3 In the similar way V = (4/3)r3 Where r is the radius which is in meters (m), therefore unitsm3 Here (4/3) is constant Here (4/3) is constant