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A circle with area X is contained in the interior of a larger circle with area X + Y. The radius of the larger circle is 3. X, Y, X + Y are in arithmetic progression. What is the radius of the smaller circle?
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The area of a circular park is 8722/3 square feet. If a pole placed at the center of the park is 37.5 feet high, approximately how many feet long is a rope which will just extend from the top of this pole to the edge of the park?
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A wheel with a 30 centimeter radius rolled down a hill at a constant speed of 20 kilometers per hour. If it rolled for 10 minutes how many complete revolutions did it make?
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A metal flag post on level ground broke at a certain point with the top part hitting the ground at a point 20 ft from the base. It was re-welded but again broke, this time at a point 5 ft lower than before, with the tip hitting the ground at a point 30 ft from the base. What is the height of the flag post?
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A 400-meter race is to be run on a track that is 400 meters long when measured along the innermost lane. The track consists of straight parallel sides, semicircular ends, and eight running lanes, each 1.23 meters wide. How far forward should the starting positions in neighboring lanes be marked so that the distance runs by each competitor the same?
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A conical paper cup with height 16 cm and a 12 cm diameter for its top is filled to the top with water. If four-fifth of the liquid is drunk by what percentage did the water level drop?
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