I tried using the formula. But I still didn't get the answer which is 1. How am I suppose to calculate please?

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1 Answer
May 8, 2018

#1#

Explanation:

For a formula

#a = (nb^cd^e)/(f^g) color(white)(...)[n\ "is constant"]#

Percentage uncertainty of #a# is given by

#%(Deltaa)/a = [(cDeltab)/b + (eDeltad)/d + (gDeltaf)/f] × 100#

Now, coming to the problem,

Volume of sphere is

#V_s = 4/3pir^3#

Here #4/3pi# is constant. So,

Percentage uncertainty of volume of sphere is

#%(DeltaV_s)/V_s = (3Deltar)/r × 100 color(white)(...)……[1]#

Volume of cube is

#V_c = a^3#

According to question, length of cube and diameter of sphere are equal. So, #a = 2r#

#V_c = (2r)^3 = 8r^3#

Here, #8# is just a constant. So,

Percentage uncertainty of volume of cube is

#%(DeltaV_c)/V_c = (3Deltar)/r × 100 color(white)(...)……[2]#

Ratio#= (%(DeltaV_s)/V_s)/(%(DeltaV_c)/V_c) = [cancel((3Deltar)/r × 100)]/[cancel((3Deltar)/r × 100)] = 1#