IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 701 - 704 of 968

Question

A man runs around a circle of radius at a speed of The time taken by him for going around it five times is ________.

Question

O is the center of a circle of diameter and is a square, if the shaded area is area of the square, then the side of square is________.

Question

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

1. Step I: Draw a line segment Take a point N outside the circle and draw a secant NOR, intersecting the circle at O and R.

2. Step II: Produce to to M such that draw a semi-circle with as diameter.

3. Step III: Draw intersecting the semi-circle at P. with N as center and MN as radius draw arcs to intersect the given circle at Q and Q’.

4. Step IV: Join NQ and NQ’. Then, NQ and NQ’ are the required tangents.

Question

A cylindrical vessel of diameter is partly filled with water. 100 lead balls are dropped in it. The rise in water level is The diameter of each ball is ________.