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.

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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 center.

Example 1

L_{L} = 2 \cdot 3.1416 \cdot 4 = 12.566 m

12.566 \cdot 50 = 628.312 m

L_{A} = 2 \cdot 3.1416 \cdot 3.5 = 21.9912m

21.9912 \cdot 50 = 1099.56m

 

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.

L_{C} = \frac {2 \cdot \pi \cdot 1.8 \cdot 146^0} {360^0} = 4.5 m

 

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.

Example 3

A = \frac {\pi \cdot 4^2 \cdot 90} {360} = 12.57 cm^2

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.

Exercise 4

A _0 = \pi \cdot 3^2 = 28.26 cm^2

Area of a square = 6^2= 36 cm^2

A = 36 - 28.26 = 7.74 cm^2

 

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.

Exercise 5

A = \pi \cdot 250^2 - 7 (\pi \cdot 1^2) = 196,327.55 m^2

 

 

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.

Exercise 6

A = \frac{\pi (8^2 - 5^2) \cdot 60} {360} = 20.42 cm^2

 

Solution of exercise 7

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

Exercise 7

A = \pi \cdot (700^2 - 5^2) = 1, 538,521.5m^2

 

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.

Exercise 8

A _ {sector} = \frac{\pi \cdot 4^2 \cdot 60}{360} = 8.38 cm^2

h = \sqrt {4^2 - 2^2} = 3.46 cm

A _{triangle} = \frac {4 \cdot 3.46}{2} = 6.93 cm^2

A _ {segment} = 8.38 - 6.93 = 1.45 cm^2

 

Solution of exercise 9

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

Exercise 9

r = \sqrt {24^2 + 7^2 = 25

A = \pi \cdot 25^2 = 1,963.50cm^2

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.

Exercise 10

Diagonal of the square= 2R

D = 8 cm             R = 4 cm

8^2 = l^2 + l^2

64 = 2l^2

l = \sqrt{32} cm

r = \frac{1}{2}

r = \frac{\sqrt{32}} {2} cm

A = \pi \cdot (4^2 - (\frac{\sqrt{32}} {2})^2) = \pi \cdot (16 - \frac{32}{4}) = 25. 13 cm^2

 

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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.