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VCE 11 General 2023

11.09 Circles, sectors and arc length

Worksheet
Circumference of a circle
1

Find the circumference of the following circles to two decimal places:

a
b
c
d
2

If the radius of a circle is 27 cm, find its circumference. Round your answer to one decimal place.

3

If the diameter of a circle is equal to 38 cm, find its circumference. Round your answer to one decimal place.

4

Find the radius of a circle with a circumference of 14 cm. Round your answer to two decimal places.

Arc length
5

For each of the following sectors, find the length of the arc to one decimal place:

a
b
c
d
e
6

The length of an arc that subtends an angle of 29 \degreeat the centre of a circle is 10 cm. Find the radius of the circle correct to two decimal places.

7

The arc formed by two points on a sphere with a radius of 2 m subtends an angle of 37 \degree at the centre. Find the length of the arc correct to two decimal places.

8

An arc formed by two points on Saturn’s surface subtends an angle of 25 \degree at Saturn’s centre. The radius of Saturn is 58\,232 km. What is the length of the arc correct to 0.1 of a kilometre?

Area of circle
9

Find the area of the following circles to one decimal place:

a
b
c
d
10

The area of a circle is 352 \text{ cm}^2.

a

If its radius is r cm, find r, round your answer to two decimal places.

b

Using the rounded value from the previous part, find the circumference of the circle. Round your answer to one decimal place.

Sectors
11

Find the perimeter of the following sectors. Round your answers to one decimal place.

a
b
12

For each sector below, calculate the following to two decimal places:

i

The perimeter

ii

The area

a
b
c
d
13

Consider the following sector. The marked angle is 344 \degree.

a

Calculate the perimeter of the sector. Round your answer to two decimal places.

b

Calculate the area of the sector. Round your answer to two decimal places.

14

Consider the following sector::

a

Calculate the perimeter. Round your answer correct to two decimal places.

b

Calculate the area. Round your answer correct to two decimal places.

Applications
15

Two identical circles of radius length 7 cm intersect at points A and B, and have their centres 12 cm apart.

a

C is the midpoint of chord AB, and is x cm away from each center. Find x.

b

Find \theta, the angle at the centre of each circle that subtends chord AB. Round your answer to two decimal places.

c

Calculate the area common to each circle. Round your answer to one decimal place.

16

A circular running track has a diameter of 23 metres. How many laps must be completed to run 1600 metres? Round your answer to one decimal place.

17

Find the area of the shaded region in the following figures. Round your answers to one decimal place.

a
b
c
d
e
f
g
h
i
j
18

Find the perimeter of the figures shown below. Round your answers to two decimal places.

a
b
c
d
e
f
19

Find the area of the following figures. Round your answers to one decimal place.

a
b
20

Calculate the perimeter of the following figures. Round your answers to one decimal place.

a
b
21

A dining table is in the shape of a rectangle plus two semicircles, as shown in the figure. What is the perimeter of the table in meters, corrected to the nearest 0.1 metre?

22

The diagram shows a piece of jewellery made out of gold:

a

Find the area of the piece. Round your answer to the nearest whole number.

b

If the gold costs \$4 per square millimetre, find the cost of the piece of jewellery.

23

The design attached is made using a large circle and two smaller circles of diameter 3\text{ cm}. Find the area of the shaded region correct to one decimal place.

24

A circular pizza of radius 8 cm is cut into sectors. Each sector is to be placed on a circular plate of radius r cm, that is just large enough to contain that sector. A sector of pizza is cut where the angle at the center is \theta, with 0 < \theta < 90 \degree. It is placed on a circular plate as shown below:

a

If the slice of pizza is \dfrac{1}{5} of the whole pizza, find the area of the slice of pizza. Round your answer to one decimal place.

b

Find the radius, r, of the plate that is needed to hold the pizza. Round your answer to one decimal place.

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Outcomes

U2.AoS4.12

use quadrilaterals, circles and composite shapes including arcs and sectors in practical situations

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