Question

The diameter of largest inscribing circle of an object is observed to be 20 mm. What would be the sphericity of the object if diameter of smallest circumscribing circle is 30 mm?

• A. 0.6
• B. 1.5
• C. 1
• D. 0.5

Hint:

Sphericity here is simply the ratio of the inscribed circle's diameter to the circumscribing circle's diameter.

Answer 1

The Correct Option is A

Step 1: For an irregular object such as a grain kernel, sphericity based on inscribed and circumscribed circles is written as \(\text{Sphericity} = \dfrac{d_i}{d_c}\), where \(d_i\) is the diameter of the largest circle that fits inside the object outline and \(d_c\) is the diameter of the smallest circle that fully encloses the object outline.

Step 2: Substitute the given values, \(d_i = 20\) mm and \(d_c = 30\) mm.

\[\text{Sphericity} = \dfrac{20}{30} = 0.667\]

Step 3: Among the given options, 0.667 sits closest to 0.6, so that is the value to pick. A sphericity value must always be less than or equal to 1 because the inscribed circle can never be larger than the circumscribing circle, which already rules out 1.5.

Why the other options fail: 1.5 is impossible since sphericity cannot exceed 1. A value of 1 would mean the object is a perfect circle in outline, which is not the case here since the two diameters differ. 0.5 is farther from the calculated 0.667 than 0.6 is.