Question 1: Calculate the radius of a circle with a circumference of 62.8 cm.

Answer: 10

Question 2: Find the area of a circle with a radius of 7 cm.

Answer: 154

Question 3: A circular pond has a diameter of 20 meters. Calculate its area.

Answer: 314

Question 4: Construct a circle with a radius of 5 cm. Label the center and plot the circle on the grid.

Answer: Circle with radius 5 cm centered at point C.

Question 5: A cyclist travels along a circular track with a radius of 50 meters. Find the distance traveled in one complete lap.

Answer: 314.16

Question 6: Explain why all points on a circle are equidistant from the center.

Answer: Because by definition, a circle is the locus of all points at a fixed distance (radius) from a fixed point (center).

Question 7: A horizontal line cuts a circle with radius 8 cm, creating a chord. If the perpendicular distance from the center to the line is 3 cm, find the length of the chord.

Answer: 10

Question 8: Calculate the coordinates of the point on a circle centered at (4, 5) with radius 6, where the point lies directly above the center.

Answer: (4, 11)

Question 9: A farmer wants to fence a circular field with a radius of 15 meters. How much fencing is needed?

Answer: 94.2

Question 10: Identify and correct the mistake: ‘The diameter of a circle is twice its radius, so the radius is half the diameter.’

Answer: The statement is correct; the radius is half the diameter.

Question 11: A dart hits a circular target with radius 12 cm at a point 5 cm from the center. How far is the dart from the edge of the target?

Answer: 7

Question 12: Challenge: A circle passes through the points (2, 3), (6, 7), and (10, 3). Find the equation of the circle.

Answer: x^2 + y^2 - 8x - 4y + 12 = 0