The problem reads as follows: You are told that the volume of a sphere isV=4r 3

Question

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

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