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

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