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The internal (di) and external (d0) diameter of a shel by sampler are 48 mm and 52 mm, respectively. The area ratio (Ar) of the sampler (in %, round off to two decimal places) is ________.
Correct answer is '17.36'. Can you explain this answer?
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The internal (di) and external (d0) diameter of a shel by sampler are ...
Calculation of Area Ratio:
The area ratio (Ar) of the sampler can be calculated by comparing the cross-sectional areas of the internal and external diameters.
Formula:
The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius.
Since we are given the diameters, we need to divide them by 2 to obtain the radii.
Step 1: Calculate the Radii:
Given:
Internal diameter (di) = 48 mm
External diameter (d0) = 52 mm
To calculate the radii, we divide the diameters by 2:
Radius of internal diameter (ri) = di/2 = 48/2 = 24 mm
Radius of external diameter (ro) = d0/2 = 52/2 = 26 mm
Step 2: Calculate the Cross-Sectional Areas:
Using the formula A = πr², we can calculate the cross-sectional areas.
Cross-sectional area of internal diameter (Ai) = π(ri)² = π(24)²
Cross-sectional area of external diameter (Ao) = π(ro)² = π(26)²
Step 3: Calculate the Area Ratio:
The area ratio (Ar) is calculated by dividing the cross-sectional area of the internal diameter by the cross-sectional area of the external diameter and multiplying by 100 to express the result as a percentage.
Ar = (Ai/Ao) * 100
Substituting the values, we get:
Ar = (π(24)² / π(26)²) * 100
The π values cancel out, so we are left with:
Ar = (24² / 26²) * 100 = (576 / 676) * 100 = 0.852 * 100 = 85.2
Therefore, the area ratio (Ar) is 85.2%.
Rounding Off:
Since the question asks for the answer to be rounded off to two decimal places, we round the answer to the nearest hundredth:
Ar = 85.2 ≈ 85.20
Thus, the area ratio (Ar) is 85.20%.
Correcting the Answer:
The correct answer given is 17.36, not 85.2. It is possible that there was an error in the calculation or in the provided answer. Please double-check the calculations or refer to the correct source for the accurate answer.
The area ratio (Ar) of the sampler can be calculated by comparing the cross-sectional areas of the internal and external diameters.
Formula:
The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius.
Since we are given the diameters, we need to divide them by 2 to obtain the radii.
Step 1: Calculate the Radii:
Given:
Internal diameter (di) = 48 mm
External diameter (d0) = 52 mm
To calculate the radii, we divide the diameters by 2:
Radius of internal diameter (ri) = di/2 = 48/2 = 24 mm
Radius of external diameter (ro) = d0/2 = 52/2 = 26 mm
Step 2: Calculate the Cross-Sectional Areas:
Using the formula A = πr², we can calculate the cross-sectional areas.
Cross-sectional area of internal diameter (Ai) = π(ri)² = π(24)²
Cross-sectional area of external diameter (Ao) = π(ro)² = π(26)²
Step 3: Calculate the Area Ratio:
The area ratio (Ar) is calculated by dividing the cross-sectional area of the internal diameter by the cross-sectional area of the external diameter and multiplying by 100 to express the result as a percentage.
Ar = (Ai/Ao) * 100
Substituting the values, we get:
Ar = (π(24)² / π(26)²) * 100
The π values cancel out, so we are left with:
Ar = (24² / 26²) * 100 = (576 / 676) * 100 = 0.852 * 100 = 85.2
Therefore, the area ratio (Ar) is 85.2%.
Rounding Off:
Since the question asks for the answer to be rounded off to two decimal places, we round the answer to the nearest hundredth:
Ar = 85.2 ≈ 85.20
Thus, the area ratio (Ar) is 85.20%.
Correcting the Answer:
The correct answer given is 17.36, not 85.2. It is possible that there was an error in the calculation or in the provided answer. Please double-check the calculations or refer to the correct source for the accurate answer.
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The internal (di) and external (d0) diameter of a shel by sampler are ...
Given:
Internal diameter of sampler, Di = 48 mm
External diameter of sampler, D0 = 52 mm
Internal diameter of sampler, Di = 48 mm
External diameter of sampler, D0 = 52 mm
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The internal (di) and external (d0) diameter of a shel by sampler are 48 mm and 52 mm, respectively. The area ratio (Ar) of the sampler (in %, round off to two decimal places) is ________.Correct answer is '17.36'. Can you explain this answer?
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