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Home > Maths I > Measure and Shape > Area and circumference of a circle

Maths I

Area and circumference of a circle

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In your General Exam you may have to work out - the circumference of a circle; the area of a circle; the perimeter of a semicircle; the area of a semicircle and the area of a combined shape including a semicircle.

The area and the circumference of a circle

Make sure that you remember that a circumference is a length and so is measured {mm}, {cm}, {m} etc. Remember as well that area is measured in square units, {mm^2}, {cm^2} etc. All of these calculations will involve the use of Pi ({\pi}) which you can take as being equal to {3.14}. A formula list is given in the exam so you don't need to remember all the formulae but you do have to remember how to use them.

The circumference of a circle

For any circle with a diameter, d, the circumference, C, is found by using the formula C = \pi d

A circle. An 8 centimetre diameter is marked. The letter C is at the top right side of the diagram.

For this circle:

C = \pi d

= 3.14 \times 8

= 25.12cm

Remember that, for any circle, the diameter is twice the radius, or {d = 2r}.

If we are told the radius instead of the diameter we use the formula - {C = 2 \pi r}

A circle. Its 3 centimetre radius is marked out. The letter c is at the top right side of the diagram.

For this circle:

C = 2 \pi r

= 2 \times 3.14 \times 3

= 18.84cm

The area of a circle

For any circle with radius, r, the area, A, is found using the formula A = \pi r^2

A circle with its 3 centimetre radius marked out. The letter c is at the top right corner of the diagram.

For this circle:

A = \pi r^2

= 3.14 \times 3 \times 3

= 28.26cm^2

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