Question:easy

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?

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Sphericity here is simply the ratio of the inscribed circle's diameter to the circumscribing circle's diameter.
  • 0.6
  • 1.5
  • 1
  • 0.5
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The Correct Option is A

Solution and Explanation

Sphericity compares how close an object's shape is to a perfect circle or sphere by comparing the biggest circle you can fit inside its outline to the smallest circle that can wrap around it completely.

Here the inside circle has a diameter of 20 mm and the outside circle has a diameter of 30 mm. Taking the ratio of inside to outside gives $20/30$, which simplifies to $2/3$, or about 0.667 in decimal form.

Because the outline can never be bigger than the circle that encloses it, this ratio always stays at or below 1, which is why an answer choice above 1 cannot be correct here. Rounding 0.667 to the nearest available answer choice lands on 0.6.

\[\boxed{\text{Sphericity} \approx 0.6}\]
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