Answer:
The percent uncertainty of the volume=[tex]\frac{15.70}{523.59} \times 100=2.99\%[/tex]
The volume of sphere with absolute uncertainty=[tex]523.59 \pm 15.7 cm^3[/tex]
Explanation:
Radius of sphere = 5 cm
Radius with uncertainty r'= [tex]5 \pm 0.05[/tex]
Volume of sphere = [tex]\frac{4}{3} \pi r^3=\frac{4}{3} \pi (r')^3[/tex]
[tex]V=\frac{4}{3} \pi (r')^3\\\frac{dV}{dr'}=4\pi (r')^2[/tex]
Where dV is the uncertainty in volume
dr' is the uncertainty in radius
[tex]dV=4\pi (r')^2 dr'\\dV=4 \pi (5)^2(0.05)\\dV=15.70\\V=\frac{4}{3} \pi (r')^3=\frac{4}{3} \pi (5)^3=523.59[/tex]
The percent uncertainty of the volume=[tex]\frac{15.70}{523.59} \times 100=2.99\%[/tex]
The volume of sphere with absolute uncertainty=[tex]523.59 \pm 15.7 cm^3[/tex]
