Year 7 Measurements - Circles

Terminology

100

distance from the centre to the edge of a circle

Radius

200

distance across the centre of a circle

diameter

300

distance around the circle

circumference

400

an area of a circle 'cut of' by a chord

segment

500

a portion of a circle enclosed by two radii and an arc

sector

diameter/radius

100

Given the radius of a circle is 5 cm, what is its diameter?

10 cm

200

Given the radius of a circle is 2.5 cm, what is its diameter?

5 cm

300

Given the diameter of a circle is 11 cm, what is its radius?

5.5 cm

400

Given the radius of a circle is 40 mm, what is its diameter?

80 mm

500

What is the formula for finding diameter, d?

d = 2r

Circumference

100

Circumference means the perimeter of a circle

TRUE or FALSE

TRUE

200

what is the formula to find circumference, C ?

  C = 2πr

300

C =  πd

TRUE or FALSE

TRUE

C = 2πr

C = πd 

400

Calculate the circumference of a circle with radius 7 cm

C = 2πr 

   = 2 x π x 7

   = 44 cm

500

Calculate the circumference of a circle with diameter 35 cm, correct to two decimal places

C = πd

   = π x 35

   = 109.96 cm

arc length

100

what is θ?

"theta", number of degrees

200

The arc length of a full circle is just its circumference

TRUE or FALSE

TRUE

The arc length of a full circle is also just its perimeter

300

What is the arc length formula?

arc length, L = θ/360° x 2πr

400

Find the arc length of a sector with radius 10 cm and 50° in two decimal places

L = θ/360° x 2πr

  = 50/360 x 2 x π x 10

  = 8.73 cm

500

Find the perimeter of a sector with 5 m radius and 300° in two decimal places

arc length, L = θ/360° x 2πr

                   = 300/360 x 2 x π x 5

                   = 26.18 m

perimeter, P = 26.18 + 5 + 5

                  = 36.18 m

Fractions of circle

100

A quadrant is half of a circle

TRUE or FALSE

FALSE

A quadrant is a quater of a circle

200

Given circumference, C = 2πr

what is formula to find the arc length, L of a semicircle? 

(Hint: semircle means half of a circle)

arc length of a semicircle = 1/2 x 2πr

                                     = πr

300

Given circumference, C = 2πr

What is formula to find the perimeter, P of a quadrant? 

(Hint: A quadrant means a quater of a circle)

arc length of a quadrant = 1/4 x 2πr

                                    = 1/2 πr

Perimeter of a quadrant = 1/2 πr + r + r

                                   = 1/2 πr + 2r

400

Find the perimeter of a semicircle with radius 10 cm in two decimal places

(Hint: C = 2πr)

Arc length of semicircle = 1/2 x 2πr

                                  = πr

                                  = π x 10

                                  = 31.42 cm

Perimeter of semicircle = 31.42 + 10 + 10

                                  = 41.42 cm

500

Find the perimeter of a quadrant with diameter 20 m in two decimal places

(Hint: C = 2πr)

Radius, r = 20/2

              = 10 m

arc length of a quadrant = 1/4 x 2πr

                                    = 1/2 πr

                                    = 1/2 x π x 10

                                    = 15.71 m

Perimeter of a quadrant = 15.71 + 10 + 10

                                   = 25.71 m