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Circle Mensuration

A line segmen...

Question

A line segment $l$ of length a cm is rotated about a vertical line L, keeping the line $l$ in one of the following three posion I) $l$ is parallel to L and at a distance of r cm. from L, (II) $l$ is perpendicular to L and its mid point is at a distance r cm, from L, (lII) $l$ and L are in the same plane and is inclined to L an angle $30^{o}$ with it mid point at a distance r cm from L. Let $A_{1}, A_{2}, A_{3}$ be the are as so qenerated. If r > (a/2), then

A

A_{1} < A_{3} < A_{2}

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B

A_{1} = A_{3} < A_{2}

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C

A_{2} < A_{1} < A_{3}

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D

A_{1} = A_{2} < A_{3}

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Solution

The correct option is D $A_{1} = A_{2} < A_{3}$

$A_{3} = π a (r - \frac{a}{4} + r + \frac{a}{4})$
Hence, $A_{1} = A_{2} = A_{3}$

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Similar questions

a_{r} > 0, r \in N

a_{1}, a_{2}, a_{3}, . . ., a_{2 n}

are in A.P. then

\frac{a_{1} + a_{2 n}}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{a_{2} + a_{2 n - 1}}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{a_{3} + a_{2 n - 2}}{\sqrt{a_{3}} + \sqrt{a_{4}}} + . . . + \frac{a_{n} + a_{n + 1}}{\sqrt{a_{n}} + \sqrt{a_{n + 1}}}

a_{r} > 0; \forall r, n \in N

a_{1}, a_{2}, a_{3}, . . . . . a_{2 n}

are in A.P, then

\frac{a_{1} + a_{2 n}}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{a_{2} + a_{2 n - 1}}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{a_{3} + a_{2 n - 2}}{\sqrt{a_{3}} + \sqrt{a_{4}}} + . . . + \frac{a_{n} + a_{n + 1}}{\sqrt{a_{n}} + \sqrt{a_{n + 1}}} =

a_{1}, a_{2}, a_{3} . . . . a_{n} \in R^{+}

a_{1} . a_{2} . a_{3} . . . . a_{n} = 1

, then minimum value of

(1 + a_{1} + a_{1}^{2}) (1 + a_{2} + a_{2}^{2}) (1 + a_{3} + a_{3}^{2}) . . . . (1 + a_{n} + a_{n}^{2})

Q. State true or false:

a_{1}, a_{2}, a_{3} \in + R

\frac{a_{1}}{a_{2}} + \frac{a_{2}}{a_{3}} + \frac{a_{3}}{a_{1}} \geq 3

a_{1}, a_{2}, a_{3}, . . . a_{n}

are in H.P then

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . a_{n}}, \frac{a_{3}}{a_{1} + a_{2} + a_{4} + . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n}}

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Circle Mensuration

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