Question

a cylinder hole 4mm in diameter and 12mm in deep in a metal block is rebored to increase the diameter to 4.12mm.estimate the amount of metal removed?

Answer 1

Answer:

The amount of metal removed => 2.89 π cubic mm

Step-by-step explanation:

The volume of cylindrical hole of radius x mm and depth 12 mm is given by

V= f(x) = 12 πx^2

⇒f ′(c) = 24πc.  

To estimate f (2.06) - f (2) :  

By law of mean,  

f (2.06) - f (2) = 0.06 f ′(c)  

= 0.06 (24 πc), 2 < c < 2.06  

Take c = 2.01  

f (2.06) - f (2) = 0.06 × 24 π × 2.01

The amount of metal removed => 2.89 π cubic mm