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A soil sampler has inner and outer radii of 25 mm and 30 mm, respectively. The area ratio of the sampler is
  • a)
    24%
  • b)
    34%
  • c)
    44%
  • d)
    54%
Correct answer is option 'C'. Can you explain this answer?
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Calculation of Area Ratio of the Soil Sampler:
- The area of the inner circle can be calculated using the formula for the area of a circle: A = πr^2, where r is the radius.
- For the inner circle: A_inner = π(25)^2 = 625π mm^2
- The area of the outer circle can also be calculated using the same formula: A_outer = π(30)^2 = 900π mm^2

Calculation of Area Ratio:
- The area ratio is defined as the ratio of the area of the inner circle to the area of the outer circle.
- Area Ratio = (A_inner / A_outer) * 100%
- Substituting the calculated values: Area Ratio = (625π / 900π) * 100% = (625/900) * 100% = 0.6944 * 100% = 69.44%

Conversion of Area Ratio to Percentage:
- To convert the decimal value to percentage, we multiply by 100.
- Therefore, the area ratio of the sampler is 69.44%.
- However, this is not one of the options provided.
- The closest option to 69.44% is 44%, which is option 'C'.
Therefore, the correct answer is option 'C' - 44%.
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