Circumference, area of circles & sectors

The diagram below shows a sketch of a circle that fits exactly inside a square.

The radius of the circle is 5 cm.

Calculate the total area of the shaded regions. Give your answer as a decimal.

You must show all your working.

The diagram below shows a sketch of a circle that fits exactly inside a square.

The radius of the circle is 5 cm.

Calculate the total area of the shaded regions. Give your answer as a decimal.

You must show all your working.

The diagram shows a sector of a circle with centre O and radius 29 cm.

The area of the sector is 756 cm². AOB = x°.

Calculate the value of x.

You must show all your working.

The diagram shows a solid cylinder with radius 10 cm.

The total surface area of the solid cylinder is 1570·8 cm².

Find the height of the cylinder.

The diagram shows a solid cylinder with radius 10 cm.

The total surface area of the solid cylinder is 1570·8 cm².

Find the height of the cylinder.

Calculate the size of angle x.

Hence, calculate the total area of the shape.

Calculate the area of a circle with a radius of 8·7 cm.

Give your answer in cm², correct to the nearest whole number.

Calculate the circumference of a circle with a radius of 38 cm.

Give your answer in cm, correct to 2 significant figures.

The diagram shows two circles that fit in a rectangle.

The centre of the small circle is directly below the centre of the large circle. The diameter of the small circle is 8 cm. The radius of the large circle is 2 cm greater than the radius of the small circle.

Calculate the total area of the shaded parts of the rectangle.

The diagram shows two circles that fit in a rectangle.

The centre of the small circle is directly below the centre of the large circle. The diameter of the small circle is 8 cm. The radius of the large circle is 2 cm greater than the radius of the small circle.

Calculate the total area of the shaded parts of the rectangle.

The diagram below shows a semicircle, with radius r, drawn inside a trapezium.

The area of the semicircle is 77 cm².

The semicircle touches the line AB. AB = 22 cm.

Calculate the area of the trapezium ABCD.

The diagram below shows a semicircle, with radius r, drawn inside a trapezium.

The area of the semicircle is 77 cm².

The semicircle touches the line AB. AB = 22 cm.

Calculate the area of the trapezium ABCD.

ABCDE is a regular pentagon with sides of length 11 cm. CDE is a sector of a circle with centre D and radius 11 cm. The two shapes are joined together, as shown below.

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Calculate the length of the arc CE shown in the diagram.

You must show all your working.

In a shape similar to the one shown on the previous page, the regular pentagon has sides of length 671 cm.

Complete the following statement.

Total area of new shape = ………………………… × total area of original shape

You must show all your working.

A, B and C are points on the circumference of a circle with centre O.

The length of BC is 10 cm. The diameter of the circle is 18 cm.

Calculate the shaded area.

You must show all your working.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A, B and C are points on the circumference of a circle with centre O. The length of BC is 10 cm. The diameter of the circle is 18 cm.

Calculate the shaded area.

You must show all your working.

The diagram shows a triangle ABC and a circle with centre C. The points B and D lie on the circumference of the circle.

The length of the line AB is 19 cm. The length of the line AC is 29 cm. The radius of the circle is xcm.

Calculate the area of the shaded sector BCD.

The diagram shows a triangle ABC and a circle with centre A.

The points B and D lie on the circumference of the circle.

The length of the line AC is 27 cm. The area of triangle ABC is 112 cm².

Calculate the area of the shaded region.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A circle with centre O is shown below. The radius of the circle is 7·3 cm.

Calculate the perimeter of the shaded region.

You must show all your working.

In the diagram below, ABCD is a rectangle with AB = 5 cm.

ABP is a quarter of a circle with centre A. AP = PD.

Calculate the area of the shaded section shown above.

You must show all your working.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

In the diagram below, ABCD is a rectangle with AB = 5 cm. ABP is a quarter of a circle with centre A. AP = PD.

Calculate the area of the shaded section shown above.

You must show all your working.

A circle has radius r cm, where r is an integer.

The side of a square is of length xcm.

If the circle and square have the same area, explain why x cannot be an integer.

You should consider algebraic expressions in your answer.

The diagram shows a sector of a circle with centre O and radius 7 cm.

Calculate the perimeter of the sector OAB.

In the diagram below, AC and BD are diameters of a circle, centre O.

AO = 30 cm and AOB = 20°.

A second circle has an area which equals the total shaded area above.

Calculate the radius of the second circle.

A and B are points on a circle with centre O.

Calculate the length of the arc AB shown below.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

AB is the diameter of a circle, centre O, with radius OA = 4·2 cm. ABCD is a square.

Calculate the area of the shaded region.

You must show all your working.

A cone is joined to a cylinder, as shown below.

The cone has a base radius of 11 cm and a slant height of 13 cm. The cylinder has the same radius, 11 cm, and a height of 17 cm.

Calculate the total surface area of the composite solid.

ABC represents the sector of a circle with radius 7 cm and centre A, as shown below. BAC = x°, AD = 3 cm and BD = 6 cm.

Find the area of the shaded region BCD.