Question

The radius of a sphere was measured and found to be 20 cm with a possible error in measurement of at most 0.02 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere

Answer 1

Answer:

D(V)  = 100,48 cm³

Step-by-step explanation:

The volume of a sphere is:

V(s) = 4/3 π*r³

Where r is the radius of the sphere

If we take derivative of V  respect r

D(V)/ dr  =  4/3*3*π*r²    ⇒ D(V)/ dr  = 4*π*r²   ⇒ D(V) =  4*π*r²*dr

We know:

r = 20 cm     and   dr  =  0,02  ( at most)

Then

D(V)  = 4*π*(20)²*0.02  cm³

D(V)  = 32*π      

D(V)  = 100,48 cm³