For each of the following sectors, find the exact length of the arc (in terms of \pi):
A sector of a circle of radius 29 \text{ m} is formed from an angle of size 131 \degree.
A sector of a circle of radius 5 units is formed from an angle of size 318 \degree.
Find the length of the following arcs, rounded to two decimal places:
A sector of a circle of radius 7 \text{ cm} is formed from an angle of size 41 \degree.
Consider the following quadrant:
Find the length of the arc in exact form.
Find the total perimeter of the quadrant in exact form.
Consider the following figure:
Find the exact length of the circumference of the whole circle.
Find the exact length of the arc of the quadrant.
Find the perimeter of the quadrant. Round your answer to two decimal places.
Find the perimeter of each of the following sectors, rounding your answers to two decimal places:
A sector of radius 14 \text{ cm} and angle of 65 \degree.
A sector of radius 3.2 \text{ m} and angle of 145 \degree.
A sector has radius 36 \text{ m} and an angle of 55 \degree.
Find the perimeter of the sector. Round your answer to two decimal places.
Find the perimeter of the sector. Round your answer to two decimal places.
Find the areas of the following figures in exact form:
Calculate the area of the following sectors, rounding your answers to one decimal place:
The area of the circle is 10 \text{ cm}^2.
Find the area of the shaded sector. Round your answer to two decimal places.
Find the exact area of a semicircle with a radius of 15 \text{ cm}.
Find the area of the sector of a circle of radius 16 \text{ cm} if the sector subtends an angle of 78 \degree at the centre. Round your answer to two decimal places.
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.
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.
Find the area that the black icing covers on the removed slice (both the top and side). Round your answer to one decimal place.
Find the area that the red icing covers on the remaining cake (both the top and side). Round your answer to one decimal place.
The diagram shows a piece of jewellery made out of gold:
Find the area of the piece. Round your answer to the nearest whole number.
If the gold costs \$4 per square millimetre, find the cost of the piece of jewellery.
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.
The diagram shows the sectors of two concentric circles with common centre O
where \angle{O} = 45 \degree, OR = 8 \text{ cm}, and OQ = 12 \text{ cm}:
Calculate the area of the shaded region between the two circular arcs, correct to one decimal place.
Calculate the perimeter of the shaded region, correct to one decimal place.
