# Worksheet: Area and Circumference of a Circle

In this worksheet, we will practice identifying when to use the circumference and area formulas of circles, including arc lengths and sector areas.

Q1:

The radius of a circle is 7 cm and the central angle of a sector is . Find the perimeter of the sector to the nearest centimetre.

Q2:

The radius of a circle is 21 cm and the angle of a sector is . Find the area of the sector giving the answer to the nearest square centimetre.

• A 151 cm2
• B 23 cm2
• C 4‎ ‎055 cm2
• D 473 cm2
• E 193 cm2

Q3:

The diameter of a circle is 78 cm and the arc length of a sector is 22 cm. Find the area of the sector, giving your answer to the nearest square centimetre.

Q4:

The area of a circular sector is 3‎ ‎872 cm2 and the arc length is equal to the radius. Find the perimeter giving the answer to the nearest centimetre.

Q5:

A circle has a radius of 42 cm, where and are two radii in the circle, and . Determine the area of the circular sector to the nearest square centimetre.

Q6:

is an equilateral triangle with a side length of 66 cm. An arc is drawn from a circle with centre cutting at point , at point and touching at point . Find the area of the part of the triangle bounded by , , and the arc giving the answer to two decimal places.

Q7:

A pendulum of length 26 cm swings . Find the length of the circular pathway that the pendulum makes giving the answer in centimetres in terms of .

• A cm
• B cm
• C cm
• D cm

Q8:

With circles and touching at , the shaded area is 331 cm2. Given that , determine the sum of the two radii correct to the nearest hundredth.

Q9:

Given that the area of a circular sector is of the area of a circle. Find, in radians, the central angle, correct to one decimal place.

Q10:

Find the circumference of a circle whose area is 9.625 cm2. Use .

Q11:

is the diameter of a semicircle of length 36 cm and . Find the area of the shaded part of the diagram giving the answer to two decimal places.

Q12:

The area of a circular sector is 122.5 and the length of the arc is 5 cm. Find the perimeter of the sector giving the answer to the nearest centimetre.

Q13:

Answer the following questions for the circle shown.

Work out the area of the circle giving your answer to two decimal places.

Q14:

Answer the following questions for the circle shown.

• A
• B
• C
• D
• E

Work out the area of the circle giving your answer in terms of .

• A
• B
• C
• D
• E

Q15:

The radius of a circle is 37 cm and the area of a sector is 555 cm2. Find the length of the arc giving the answer to the nearest centimetre.

Q16:

The radius of a circle is 40 cm and the angle of a sector is 2.9 rad. Find the area of the sector giving the answer to the nearest square centimetre.

Q17:

The circle of centre and radius is divided into four sectors, each of perimeter 75 and arc length 33. Determine the radius and the area of each sector . Use 3.14 as an approximation value for .

• A ,
• B ,
• C ,
• D ,

Q18:

and are two chords in the circle where and . Find the area of the minor sector giving the answer to the nearest square centimetre.

Q19:

The area of a circle is 1‎ ‎539 cm2 and the arc length of a sector is 36 cm. Find the area of the sector giving the answer to the nearest square centimetre.

Q20:

A circle has a radius of 4 cm and a segment has a central angle of . Find the area of the segment giving the answer to two decimal places.

Q21:

Determine the circumference of a circle whose area is 88‎ ‎704 cm2, taking .

Q22:

What is the circumference of a circle whose area is cm2. Express your answer in terms of .

• A cm
• B cm
• C cm
• D cm

Q23:

Answer the following questions for the circle shown.

Work out the area of the circle giving your answer to two decimal places.

Q24:

The perimeter of a circular sector is 58 cm and the arc length is 26 cm. Find the area of the circle giving the answer to the nearest square centimetre.

Q25:

Determine, in terms of , the circumference of a circle whose area is .

• A
• B
• C
• D
• E