Help your students prepare for their Maths GCSE with this free area of a circle worksheet of 20+ questions and answers
Area is the amount of space covered by a 2D shape and is measured in square units – metric units of area include mm², cm² and m².
The formula for the area of a circle is πr², where r is the radius of the circle. If the radius is given, we need to square it and multiply it by π to find the area of the circle. If the diameter of a circle is given instead of its radius, we need to divide the diameter by 2 to find the radius, then proceed as above. If the area of a circle is given, students may be asked to work backwards to find the length of the radius. Here, we need to divide by π and square root.
Students may sometimes be asked to leave their answer in terms of π; if this is not the case they will need to round the decimal answer to a given number of decimal places.
Application of this formula is fairly straightforward, but care must be taken as students can easily confuse this with the formula for the circumference of a circle.
This topic can be extended further to the area of a semicircle and other fractions of a circle. Word problems may require students to apply knowledge of compound shapes – for example, finding the area of a parallelogram with two circles cut from it, by finding the area of each circle and subtracting from the area of the parallelogram.
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