 # Calculate Lengths of Arcs and Perimeters

In this worksheet, students calculate lengths of arcs and perimeters of circular shapes. Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Calculate Arc Lengths, Angles and Areas of Sectors of Circles

Difficulty level:   ### QUESTION 1 of 10

This worksheet is about calculating the lengths of arcs. Remember, arc length = 2 × r × × for radius r, angle at centre = 360

This formula works because  2 × r × is the circumference of the whole circle. /360 is the fraction of the circle represented by the arc.

Calculate the arc length of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 R = 24 cm

Θ = 11.5 °

Arc length = ____ cm

Calculate the arc length of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 R = 22.5 cm

Θ = 9°

Arc length = ____ cm

Calculate the perimeter of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 R = 6 cm

Θ = 8.5°

Perimeter = ____ cm

Calculate the perimeter of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 a = 10 cm

b = 5 cm

r = 8.9 cm

φ = 40°

Perimeter = ____ cm

Calculate the perimeter of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 a = 13 cm

b = 3 cm

r = 3.4 cm

φ = 40°

Perimeter = ____ cm

Calculate the perimeter of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 R = 5 cm

Θ = 8 °

Perimeter = ____ cm

Calculate the perimeter of the given shape to 3 sig. figs. R = 9.5 cm

Θ = 10 °

Perimeter = ____ cm

Calculate the perimeter of the given shape to 3 sig. figs. a = 15 cm

b = 6 cm

r = 9.9 cm

φ = 55°

Perimeter = ____ cm

Calculate the perimeter of the given shape to 3 sig. figs. R = 11.5 cm

Θ = 10 °

Perimeter = ____ cm

Calculate the perimeter of the given shape to 3 sig. figs. R = 20 cm

Θ = 7 °

Perimeter = ____ cm

• Question 1

Calculate the arc length of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 R = 24 cm

Θ = 11.5 °

Arc length = ____ cm

4.82
EDDIE SAYS
 2 × 24 × × 11.5 360
• Question 2

Calculate the arc length of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 R = 22.5 cm

Θ = 9°

Arc length = ____ cm

3.53
EDDIE SAYS
 2 × 22.5 × × 9 360
• Question 3

Calculate the perimeter of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 R = 6 cm

Θ = 8.5°

Perimeter = ____ cm

12.9
EDDIE SAYS
Remember to include the two radii.
 2 × 6 × × 8.5 + 6 + 6 360
• Question 4

Calculate the perimeter of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 a = 10 cm

b = 5 cm

r = 8.9 cm

φ = 40°

Perimeter = ____ cm

31.2
EDDIE SAYS
Remember to include the three sides.
 2 × 8.9 × × 40 + 10 + 10 + 5 360
• Question 5

Calculate the perimeter of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 a = 13 cm

b = 3 cm

r = 3.4 cm

φ = 40°

Perimeter = ____ cm

31.4
EDDIE SAYS
Remember to include the three sides.
 2 × 3.4 × × 40 + 13 + 13 + 3 360
• Question 6

Calculate the perimeter of the given shape to 3 sig. figs.

 Remember, arc length = 2 × r × × for radius r, angle at centre = 360 R = 5 cm

Θ = 8 °

Perimeter = ____ cm

10.7
EDDIE SAYS

Remember to include the two radii.

 2 × 5 × × 8 + 5 + 5 360
• Question 7

Calculate the perimeter of the given shape to 3 sig. figs. R = 9.5 cm

Θ = 10 °

Perimeter = ____ cm

20.7
EDDIE SAYS
Remember to include the two radii.
 2 × 9.5 × × 10 + 9.5 + 9.5 360
• Question 8

Calculate the perimeter of the given shape to 3 sig. figs. a = 15 cm

b = 6 cm

r = 9.9 cm

φ = 55°

Perimeter = ____ cm

45.5
EDDIE SAYS

Remember to include the three sides.

 2 × 9.9 × × 55 + 15 + 15 + 6 360
• Question 9

Calculate the perimeter of the given shape to 3 sig. figs. R = 11.5 cm

Θ = 10 °

Perimeter = ____ cm

25.0
EDDIE SAYS

Remember to include the two radii.

 2 × 11.5 × × 10 + 11.5 + 11.5 360
• Question 10

Calculate the perimeter of the given shape to 3 sig. figs. R = 20 cm

Θ = 7 °

Perimeter = ____ cm

42.4
EDDIE SAYS
Remember to include the two radii.
 2 × 20 × × 7 + 20 + 20 360
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