Question

The radius of a 16 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.05 inch. In order to solve this problem you have to use linear approximation or differentials in order to determine the possible error in the volume of the cylinder. It is important to use units while solving.

Answer 1

DV(x) = ± 20.96 in³

Explanation:

The volume of the cylinder is:

V(c) = π*r²*h where r is the radius of the cicular base and h the height

we must assume thre is not error when measuring the height ( 16 in)

Taking derivatives in both sides of the mentioned formula

V(x) = π*x²*h

DV(x) / dx = π* 2x*h ⇒ DV(x) = π* 2x*h*dx

We already know x (radius = 4 in h = 16 in and dx = ± 0.05 in

DV(x) = 3.14*2*4*16*0,05

DV(x) = ± 20.96 in³