Assertion -If the outer and inner diameter of a circular path is 10 m and 6 m- then the area of the path is 16 - m2- Reason- If R and r be the radius of outer and inner circular path respectively then area of path - R2-r2

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Standard VII

Mathematics

Area of Circle

Assertion :If...

Question

Assertion :If the outer and inner diameter of a circular path is $10 m$ and $6 m$ , then the area of the path is $16 π m^{2}$ . Reason: If $R$ and $r$ be the radius of outer and inner circular path respectively then area of path $= π (R^{2} - r^{2})$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Both assertion and reason are correct. Also, Reason is the correct explanation of the assertion.
Area of the path $= π (R^{2} - r^{2})$

$= π [{(\frac{10}{2})}^{2} - {(\frac{6}{2})}^{2}]$
$= π (25 - 9)$

$= 16 π m^{2}$

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Assertion :If the outer and inner diameter of a circular path is 10 m and 6 m, then the area of the path is 16π m2. Reason: If R and r be the radius of outer and inner circular path respectively then area of path =π(R2−r2)

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionBoth assertion and reason are correct. Also, Reason is the correct explanation of the assertion.Area of the path =π(R2−r2) =π[(102)2−(62)2] =π(25−9) =16π m2

Assertion :If the outer and inner diameter of a circular path is $10 m$ and $6 m$ , then the area of the path is $16 π m^{2}$ . Reason: If $R$ and $r$ be the radius of outer and inner circular path respectively then area of path $= π (R^{2} - r^{2})$