 4.06 Area of circles and sectors

Worksheet
Area of circles
1

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

a

A circle with radius 9\text{ cm}

b

A circle with diameter 24\text{ cm}

2

The radius of a circular baking tray is 10\text{ cm}. Find its area correct to two decimal places.

3

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

a
b
c
d
4

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

a

b

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

5

Find the shaded area of the following figures, correct to one decimal place:

a
b
Area of sectors
6

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

a
b
c
d
e
f
7

Consider the given circle with radius 1.79 \text{ cm}. Find the area of the shaded sector, correct to one decimal place.

8

Find the area of the sector of a circle of radius 16 cm, if the sector subtends an angle of 78 \degree at the centre. Round your answer to two decimal places.

9

For each of the given sectors:

i

Find the perimeter of the sector, correct to two decimal places.

ii

Find the area of the sector, correct to two decimal places.

a
b
c
d
e
f
g
h
i
j
k
l
10

The diagram shows an arc JK of a circle, with centre O. The radius of the circle measures 15 \text{ cm} and the arc measures 12 \text{ cm} in length.

a

Find \angle JOK to the nearest degree.

b

Find the exact area of the sector.

11

The area of the sector below is 2960.92\text{ m}^2.

a

Find the length of the radius, correct to one decimal place.

b

Hence, find the perimeter of the sector, correct to one decimal place.

12

Find the area of the shaded region in the given sector. Round your answer to one decimal place.

13

Find the area of the shaded figure shown, correct to two decimal places.

Applications
14

A large 17 \text{ m} long sprinkler is placed in a crop field, with one end fixed and the other end free to move. As it rotates, it waters everything underneath it.

If the sprinkler has rotated 86\degree since the farmer left, find the area of the crop field it has watered. Round your answer to one decimal place.

15

Roald makes a lady beetle cake with a diameter of 24 \text{ cm} and a height of 10 \text{ cm}. Roald removes a slice of the cake with an angle measure of 45\degree.

a

Find the area that the black icing covers on the removed slice (both the top and side). Round your answer to one decimal place.

b

Find the area that the red icing covers on the remaining cake (both the top and side). Round your answer to one decimal place.

16

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.

17

A security light shines on an adjacent fence at a distance of 10 metres from the light bulb.

Find the area on which this security light shines.