Additional investigations

Dalmatian Day: Cut various circles from paper measuring 9 inches by 12 inches. What's the area of the circles and the percent of paper wasted after cutting out the circles?

Target Areas: Determine the area of a target formed by concentric circles.

Inscribed Circle: Finding an estimation for the area of a circle.

Summing Circles: Finding the cumulative area of shrinking circles.

Dividing Pizza: Compare slices of pizza from pizzas with different diameters.

Segment Areas: Determine the measure of the central angle of a circle that will make the shaded region's area 1/ 4 of the entire circle's area.

Circle Inscribed in a Semicircle: Compare attributes of a circle that is inscribed in a semicircle to attributes of that semicircle.

Surrounding Squares: Find a method that will construct a square that has the same area as the area of a given circle.

Surface Area: Relate the surface area of a sphere to the area of a circle.

Walking Around the World: Compare the distance a man's head travels to the distance his feet travel when he walks around the world.

Wrapping Around the World: How much string is needed to wrap around the world?

N-Sided Circle?: Compare the perimeters of polygons to the circumference of a circle.

Rationalize Pi: Approximate pi with a rational number.

A Common Ratio: Compare the ratio of the circumference (C) and the diameter (d) of several circles.

Running in Circles: Can Peanut the dog get a drink of water if his bowl of water is 20 feet away from the stake he is tied to?

The Bicycle Problem: Compare the radius of a bicycle wheel to the number of revolutions the wheel makes.

Grazing for Mooey: How many square meters of grazing ground does Mooey the cow have?

Squaring the Circumference: Find a method that will construct a square that has the same perimeter as the circumference of a given circle.

Opposite Angles: Find a relationship between the opposite angles in a quadrilateral inscribed in a circle.

Inscribed in a Semi-Circle: Examine the angles inscribed in a semicircle.

Inscribed in a Triangle: Construct a circle inscribed in a triangle so that it will always remain inscribed in the triangle.

Perpendicular Bisectors: Describe the significance of the perpendicular bisectors of two segments that have endpoints on a given circle.

Passing thru the Center: What is the relationship between two circles relate that pass through each other's centers?

Equidistant Chords: Determine the relationship between two segments that have endpoints on a circle if the segments are the same perpendicular distance away from the center of the circle.

Quarter-Circle Spiral: What relationships can you find between the radii of quarter circles?

Inscribed Parallelogram: What must be true about a parallelogram that is inscribed in a circle?

Locus of Reflection: Trace the path of a reflected point to determine a pattern and the reason the pattern occurs.

Packing Circles: Investigate how many circles you can pack inside a square.

Tangent Lines to a Circle: How does a tangent line relate to the radius that intersects the tangent line?

Wheeling Along: Determine the number of times a smaller wheel must revolve before a larger wheel begins rolling if the wheels will eventually meet under certain conditions.

Pizza Pizzazz: Thomas complains the prices of pizzas at a restaurant are unfair. Why?

Submit your idea for an investigation to InterMath.