8.13 Circles and Angles

Find the circumference of a circle with radius 8 cm. Use $\pi = 3.14$; 1 d.p.

Find the area of a circle with radius 6 cm. Use $\pi = 3.14$; 1 d.p.

Identify each as acute, right, obtuse, straight, or reflex: 35°, 90°, 120°, 180°, 250°.

Find the diameter of a circle with circumference 62.8 cm. Use $\pi = 3.14$; 1 d.p.

A pizza has diameter 30 cm. Find its area. Use $\pi = 3.14$; 1 d.p.

Is the shape concave or convex? Octagonal shape with all interior angles < 180°.

A circle has radius 7 cm. Find the (a) diameter, (b) circumference, (c) area. Use $\pi = 22/7$.

What is the value of $\pi$ to 3 decimal places?

A circle has radius 10 cm. Find the (a) circumference and (b) area. Use $\pi$ in your answer.

Classify each angle: (a) 35°, (b) 95°, (c) 175°, (d) 200°.

A circle has diameter 14 cm. Find (a) radius, (b) circumference, (c) area. Use $\pi = 3.14$; 1 d.p.

A circular pizza has area 314 cm² (use $\pi = 3.14$). Find its radius.

Find the perimeter of a semicircle of radius 7 cm. Use $\pi = 3.14$; 1 d.p.

A circle is inscribed in a square of side 8 cm. Find the area of the circle (use $\pi = 3.14$).

Find the area of the sector with angle 60° and radius 9 cm.

Find the arc length of a sector with angle 120° and radius 9 cm.

A bicycle wheel has diameter 60 cm. Find the distance travelled in 1 revolution (in m).

A clock's minute hand is 12 cm long. Find the distance the tip travels in 15 minutes.

A circular pond has diameter 10 m. Find (a) the perimeter, (b) the area covered by the pond. (Use $\pi = 3.14$.)

Classify the shape: a polygon has 6 angles, all measuring 120°. Is it convex or concave? Identify the shape.

A circle has radius 3 m. Find its area in (a) m² and (b) cm². Use $\pi = 3.14$; 1 d.p.

A circle has radius $(x + 2)$ cm and area $9\pi$ cm². Find $x$.

A circular flower bed has area $25\pi$ m². (a) Find the radius. (b) Find the circumference (use $\pi = 3.14$; 1 d.p.).

A composite shape: a rectangle 10 cm by 6 cm with a semicircle of diameter 6 cm attached to one short side. Find the perimeter (use $\pi = 3.14$; 1 d.p.).

A square is inscribed inside a circle. The circle has area $50\pi$ cm². Find (a) the radius, (b) the side of the square.

A circle is inscribed in a square of side 10 cm. Find the area between the square and the circle.

A semicircle has diameter 10 cm. Find its (a) area, (b) perimeter (use $\pi = 3.14$; 1 d.p.).

Two concentric circles have radii 8 cm and 5 cm. Find the area of the annulus (the ring between them).

Three congruent circles, each of radius 5 cm, are arranged in a row touching each other. Find the total perimeter (of the visible outline if joined as one shape).

A pizza is cut into 8 equal slices. Find the angle of each slice. If the pizza has radius 15 cm, find the area of one slice.

A flower bed is a square with a quarter-circle attached to one corner. The square is 6 m by 6 m, and the quarter-circle has radius 6 m (occupying the area outside the square). Find the total area and total perimeter.

A running track consists of a rectangle 80 m by 40 m, with semicircles of radius 20 m at each short end. Find the total perimeter and area.

A square has area equal to that of a circle of radius 6 cm. Find the side length of the square.

A circle has circumference $C$. By how much does its circumference increase if its radius increases by 1 cm?

Three identical circles of radius 5 cm are arranged so each touches the other two. Find the area of the curvilinear triangle in the middle (between the three circles).

A circle's area increases by 21%. By what percentage does its radius increase?

A circular pond of radius 10 m is to be surrounded by a path of width 1 m. Find the area of the path.

A circle is inscribed in a regular hexagon of side 6 cm. (a) Find the radius of the circle. (b) Find the area of the hexagon and the circle, and the area between them.

A bicycle wheel has diameter 70 cm. The bike travels 1 km. How many full revolutions does the wheel make?

A clock's minute hand is 8 cm long. (a) Find the distance the tip travels in 1 hour. (b) Find the area swept by the hand in 15 minutes.