Area
Circumference
Mixed Problems
Sector and Arc
challenging problems
100

I have a circle with 0.5 inches as a radius. What is the area, correct to 2dp? 

what is 0.79 in2

100

Calculate the circumference of a car tire, in terms of 

π, with a radius of 18 inches.

What is 36π 

100

Accurately describe the following terms:

Radius

Diameter

Arc

Response given

100

Find the area of the sector, given that the central angle is 150 degrees and the radius is 6cm. Round your answer to the nearest whole number

What is 47cm2

100

I have a semicircle with a radius of 6cm. What is the area of the semicircle?

What is 56.56cm2

200

What is the area of a semicircle if the radius is 6.78cm? 

What is 72.17cm2

200

What is the circumference of a circle with 56.64cm as diameter?  Round to the nearest whole number

What is 178 cm

200

Explain what is area and circumference 

Listen to response

200

OAB is a sector of a circle, center O.

Angle AOB =60 degrees.

OA = OB = 12cm

Work out the length of the arc AB, give your answer in terms of pi

What is 4π 

200

The circumference of a circle measures 19.5cm. Work out the length of the diameter of the circle. 

What is 6.2cm

300

What is the area of a circle with a diameter of 6.78in? 

Correct to 1 decimal place. 

What is 36.1in2

300

A circular plate has a circumference of 37.7cm. Calculate the diameter of the plate to the nearest whole number

What is 12cm

300

I have a circle with an area of 5467.65cm2. What is the circumference? Round all answers to 2 decimal places.

What is 262.06cm?

300

Calculate the area of the sector, given that the radius =13cm and the central of the sector is 150 degrees.

Give your answer to 3 significant figures

What is 221cm2

300

The circular base of a chair is 9cm in radius, and the pole is 0.76cm in radius. What is the area of the base showing?

What is 252.19 cm2

400

What is the area of a circle in terms of pi, that has a radius of 3cm?

What is 9π

400

A circle has a circumference of 40cm. Work out the area of the circle. Round all answers to 1 d.p

What is 128.6cm2

400

What is the area of a circle if the circumference is 10? Round all answers to 2 decimal places.

What is 7.94cm2

400

Given that the area of a sector is 38.4cm2 and its radius is 9.2cm, find the measure of the central angle, to the nearest degree.

What is 52 degrees

400

A circle has a radius of 5.6cm, work out the perimeter of the semicircle.


What is 28.78cm

500

A circle has an area of 64π cm2. Work out the radius of the circle.

What is r = 8cm

500

A primary school has a running track. 

It has two straights of 50 meters. 

Also there are two 'bends' that are semicircles with diameter 30 meters.

Work out the distance around the running track.

What is 194.2m

500

What is the circumference of a circle with the area of 465.45cm2? Round your answer to two decimal places.

What is 76.43cm

500

The arc length of a sector is 15cm, with a radius of 10cm. Calculate the area of the sector, to the nearest whole number

What is 75cm2

500

Work out the perimeter of a quarter-circle with radius 7cm.

What is 24.99cm


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