Question

A taper hole is inspected using a CMM, with a probe of 2 mm diameter. At a height, $\text{Z=10 mm}$ from the bottom, 5 points are touched and a diameter of the circle (not compensated for probe size) is obtained as 20 mm. Similarly, a 40 mm diameter is obtained at a height $\text{Z=40 mm.}$ The smaller diameter (in mm) of hole at $\text{Z = 0}$ is

• A. $15.542$
• B. $15.334$
• C. $13.334$
• D. $15.442$

Answer 1

The correct option is C $13.334$

$tan\theta =\frac{CB}{AB}=\frac{10}{30}=\frac{1}{3}$


$\text{Now,}tan\theta =\frac{x}{10}$

$\frac{1}{3}=\frac{x}{10}$

$\Rightarrow x=\frac{10}{3}mm=3.33mm$

$\text{So, Diameter at}z=0,$

$=20-2x=20-2\times 3.33=13.334mm$