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Calculate Lengths of Arcs and Perimeters

In this worksheet, students calculate lengths of arcs and perimeters of circular shapes.

'Calculate Lengths of Arcs and Perimeters' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

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

Difficulty level:  

down

Worksheet Overview

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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

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