IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 748 - 752 of 968

If the radii of the circular ends of a conical bucket are and and the height is the capacity of the bucket is________.

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Give below are the steps of construction of (without using the center of the circle radius ) two tangents to the circle from point A.

1. Step I: Draw a line segment Take a point A outside the circle and draw a secant ACD, intersecting the circle at C and D.
2. Step II: Produce to to B such that draw a semi-circle with BD as diameter.
3. Step III: Draw intersecting the semi-circle at E. with A as center and BA as radius draw arcs to intersect the given circle at S and S՚.
4. Step IV: Join AS and AS՚. Then, AS and AS՚ are the required tangents.

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In the given figure, O is the center of the circle, then is ________.

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The perimeter of a sector of a circle of radius is The area of the sector is________.

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Given below are the steps of construction of a pair of tangents to a circle of radius which are inclined to each other at an angle of . Find which of the following step is wrong.

1. Step I: Take a point O on the paper and draw a circle of radius
2. Step II: Produce to such that
3. Step III: Taking as the center draw a circle of radius suppose it cuts the circle drawn in step I at P and Q.
4. Step IV: Join and to get desired tangents.

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