Circumference and area of circles

Task goals

• Define a circle as the locus of points in a plane at a fixed distance (the radius) from a fixed centre.
• Convert between the radius and diameter of a circle.
• Calculate the circumference or area of a circle from its radius or diameter, using an approximate value of pi.
• Work backwards from a given circumference or area to find the circle's radius or diameter.
• Calculate the perimeter or area of a semicircle or quarter circle.
• Calculate the circumference or area of a circle, giving the answer exactly in terms of $\pi$, including a bicycle-wheel-style revolutions problem.
• Use the ratio between the radii of two circles to find the ratio of their circumferences or areas.
• Solve composite or real-world problems involving circles, such as the area of an annulus between two concentric circles, a shape inscribed in or around a circle, a circular sector's arc length and area, or the cost of concreting a path around a circular pond.