Exercise 1

Anne is riding a horse which is tied to a pole with a 3.5 m piece of rope and her friend Laura is riding a donkey which is 2 m from the same center point. Calculate the distance travelled by each when they have rotated 50 times around the centre.

Exercise 2

The rope that attaches a swing to a tree is 1.8 m long and the maximum difference between trajectories is an angle of 146°. Calculate the maximum distance travelled by the seat of the swing when the swing angle is described as the maximum.

Exercise 3

Find the area of a circular sector whose chord is the side of the square inscribed in a circle with a 4 cm radius.

Exercise 4

Calculate the shaded area, knowing that the side of the outer square is 6 cm and the radius of the circle is 3 cm.

Exercise 5

In a circular park with a radius of 250 m there are 7 lamps whose bases are circles with a radius of 1 m. The entire area of the park has grass with the exception of the bases for the lamps. Calculate the lawn area.

Exercise 6

Two radii (plural for radius) OA and OB form an angle of 60° for two concentric circles with 8 and 5 cm radii. Calculate the area of the circular trapezoid formed by the radii and concentric circles.

Exercise 7

A circular fountain of 5 m radius lies alone in the centre of a circular park of 700 m radius. Calculate the total walking area available to pedestrians visiting the park.

Exercise 8

A central angle of 60° is plotted on a circle with a 4 cm radius. Calculate the area of the circular segment between the chord joining the ends of the two radii and its corresponding arc.

Exercise 9

A chord of 48 cm is 7 cm from the center of a circle. Calculate the area of the circle.

Exercise 10

Calculate the area enclosed by the inscribed and circumscribed circles to a square with a diagonal of 8 m in length.

Solution of exercise 1

Anne is riding a horse which is tied to a pole with a 3.5 m piece of rope and her friend Laura is riding a donkey which is 2 m from the same center point. Calculate the distance travelled by each when they have rotated 50 times around the centre.

Solution of exercise 2

The rope that attaches a swing to a tree is 1.8 m long and the maximum difference between trajectories is an angle of 146°. Calculate the maximum distance travelled by the seat of the swing when the swing angle is described as the maximum.

Solution of exercise 3

Find the area of a circular sector whose chord is the side of the square inscribed in a circle with a 4 cm radius.

Solution of exercise 4

Calculate the shaded area, knowing that the side of the outer square is 6 cm and the radius of the circle is 3 cm.

Solution of exercise 5

In a circular park with a radius of 250 m there are 7 lamps whose bases are circles with a radius of 1 m. The entire area of the park has grass with the exception of the bases for the lamps. Calculate the lawn area.

Solution of exercise 6

Two radii (plural for radius) OA and OB form an angle of 60° for two concentric circles with 8 and 5 cm radii. Calculate the area of the circular trapezoid formed by the radii and concentric circles.

Solution of exercise 7

A circular fountain of 5 m radius lies alone in the centre of a circular park of 700 m radius. Calculate the total walking area available to pedestrians visiting the park.

Solution of exercise 8

A central angle of 60° is plotted on a circle with a 4 cm radius. Calculate the area of the circular segment between the chord joining the ends of the two radii and its corresponding arc.

Solution of exercise 9

A chord of 48 cm is 7 cm from the center of a circle. Calculate the area of the circle.

Solution of exercise 10

Calculate the area enclosed by the inscribed and circumscribed circles to a square with a diagonal of 8 m in length.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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