Tag Archives: ratio

Water in Glass Box

A glass box cm, closed on all six sides, is partially filled with colored water. When the box is placed on one of its sides, the water level is cm above the table. If the box is placed on one … Continue reading

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Two Squares

If the vertices of square are the midpoints of the edges of square , then what is the ratio of the area of square to square ? Source: NCTM Mathematics Teacher, September 2006 Solution The diagonal of square divides square … Continue reading

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Ball and Cube

Suppose that the volume of a ball is equal to times the volume of a cube. What is the ratio of the surface area of the ball to that of the cube? Source: NCTM Mathematics Teacher, September 2006 Solution Let … Continue reading

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Square in Circle

A square of maximum area is inscribed in a semicircle as shown. What percent of the area of the circle is outside the square? Source: NCTM Mathematics Teacher, January 2006 SOLUTION area of circle = area of square = area … Continue reading

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Garage Sale

Before going to a garage sale, Elise counted the money she was taking along. After an hour, she counted it again and found that she had spent exactly half of it. The number of cents she now had equaled the … Continue reading

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Tetrahedron

Four of the nonadjacent vertices of a cube form a regular tetrahedron. What is the ratio of the surface area of the cube to the surface area of the tetrahedron? Source: NCTM Mathematics Teacher, December 2005 SOLUTION Let the side … Continue reading

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Big and Small Circles

Two circles of radius are tangent to each other as shown. A line is drawn tangent to both circles. A third circle is drawn so that it is tangent to both circles and the line. The radius of this smaller … Continue reading

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Ratio of Sectors

In the figure, and are sectors of two concentric circles centered at . The length of is one-third the length of . What is the ratio of the area of the region to the area of the sector ? Source: … Continue reading

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Similar Triangles

In triangle , and . Side is extended to point so that triangle is similar to triangle . What is ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Triangle is similar to triangle Solving Cross multiply Solving Multiply the left … Continue reading

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Bookshelf

A bookshelf is inches long and contains books each inches thick. If each book were half an inch thinner, the shelf would hold six more of the same book. What is ? Source: NCTM Mathematics Teacher, February 2006 SOLUTION Substitute … Continue reading

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