Key points
饾懆 = 蟺饾挀虏 is the formulaA fact, rule, or principle that is expressed in words or in mathematical symbols. Plural: formulae. for finding the area of a circle. 蟺 is a constantA number or quantity that does not vary. and 饾挀 is the radiusThe distance from the centre of the circle to the circumference. of the circle.
The diameterThe distance across the circle, circumference to circumference, through its centre. of a circle is halved to give the radius. The value of 蟺 may be rounded to 3郯142 or 3郯14. The 蟺 button on a calculator is used in calculations. The area is given in square unitA square unit is defined as a metric unit used to measure area. For example, square metres (m虏), square centimetres (cm虏), square inches (In虏) including cm虏 and m虏.
A scientific calculator may be set to show answers in surdAn irrational number. This includes the square roots that cannot be written as an exact decimal and special values like 蟺. notation. Understanding how to use a calculator to convert between surd notation and the decimal equivalent is important.
The ability to round a number to a number of decimal places or to a number of significant figures is essential if answers are to be written to the correct degree of accuracy asked for in a question.
It may also be helpful to understand 蟺 (pi) and the circumference of a circle.
Calculating the area of a circle
To illustrate the formula for the area of a circle:
A circle can be cut into sectorA portion of a circle with a perimeter made up of two radii and an arc..
The sectors can be rearranged to form an approximateDescribing something that is not exact, but sufficiently close for it to be useful. rectangle shape. The more sectors the closer to a rectangle the shape will become.
The length of the rectangle is half the circumferenceThe distance around a circle; its perimeter., 蟺饾挀. The width of the rectangle is the radius of the circle, 饾挀. The area of the rectangle is length 脳 width, 蟺饾挀 脳 饾挀 = 蟺饾挀虏.
The formula for the area of the circle is 饾懆 = 蟺饾挀虏.
To work out the area of a circle:
Find the value of the radius. If the diameter is given, this must be halved.
Substitute the value of the radius into the formula for the area of a circle.
Multiply 蟺 by the square of the radius. This is the same as 蟺 脳 饾挀 脳 饾挀.
If necessary, round to the degree of accuracyHow precise a measurement is required, often shown as the number of decimal places or significant digits..
If using a scientific calculator, use the S
鈬
D button to convert a value given in terms of 蟺 to a decimal.
Example
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Question
Find the area of the circle, using 蟺 = 3郯142. Round the answer to three significant figures.
- The diameter of the circle is 40 cm.
- The formula for the area of a circle uses the radius.
- The radius of the circle is half of the diameter. 40 梅 2 = 20
The radius of the circle is 20 cm. - Substitute 饾挀 = 20 into the formula for the area of the circle.
- Multiply 蟺 by the square of the radius. 3郯142 脳 20虏 =1256郯8
This must be rounded to three significant figures. - The area of the circle is 1260 cm虏 to three significant figures.
Calculating the radius and diameter of a circle, when given its area
The operations used to find the area are squaring the radius, then multiplying by 蟺. The inverseWhen an operation is combined with its inverse, the number is unchanged. Multiplication and division are inverse operations. Eg, 3 脳 10 梅 10 = 3 of multiply by 蟺 is divide by 蟺. The inverse of square is square rootA square root of a number is a value that, when multiplied by itself, gives the number. Eg, 4 脳 4 = 16, so the square root of 16 is 4.
To find the radius from the area of a circle, use the inverse operations:
Divide the area by 蟺.
Find the square root.
To find the diameter, multiply the radius by 2
It may be useful to look at changing the subject.
Example
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Question
The circle has an area of 56 mm虏. Find the radius of the circle and give the answer to two decimal places.
- The formula for the area of a circle squares the radius and multiplies by 蟺. The inverse process is used to find the radius from the area.
Using 蟺 = 3郯142:
Divide the area of the circle by 蟺. 56 梅 3郯142 = 17郯82304265
Square root the value then round to two decimal places
鈭17郯82304265 = 4鈭221734554The radius of the circle is 4郯22 mm to two decimal places.
Using the 蟺 button on a calculator:
Divide the area of the circle by 蟺. 56 梅 蟺 = 17郯82535363
Square root the value then round to two decimal places
鈭17郯82535363 = 4鈭222008246The radius of the circle is 4郯22 mm to two decimal places.
Practise finding the area of a circle
Practise finding the area of a circle with this quiz. You may need a pen and paper to help you.
Quiz
Game - Divided Islands
Play the Divided Islands game! gamePlay the Divided Islands game!
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