Learn how to account the ambit and breadth of a amphitheater in agreement of π, abrogation your acknowledgment in exact form.

This assignment includes:

Created in affiliation with GCSEPod

The breadth of a amphitheater can be affected application the breadth of the radius. The ambit is the straight-line ambit from the centre of a amphitheater to its edge.

Circumference is the chat accustomed to call the ambit of a circle, and is the ambit all about its outline. The ambit of a amphitheater can be affected application the breadth of the diameter.

The bore is alert the breadth of the radius, and is the straight-line ambit from the bend of a amphitheater to the adverse bend of the circle, casual through its centre.

Before you account the breadth and ambit of a circle, you charge to accept the amount of π, a Greek letter alleged ‘pi’ (pronounced as the English chat ‘pie’).

π is an aberrant cardinal which agency that if you address out the decimal anatomy of π, the decimal will not abolish and the ethics in the cardinal will not chase a pattern.

π cannot be accounting as a fraction, and if you use π as a decimal it has to be angled and accordingly the adding will not be exact.

As a symbol, π is acclimated in maths to represent the amount 3.14 (to 2 decimal places) that is bare back alive with circles.

You will generally be asked to account ethics involving circles, application the attribute π in the result.

This is alleged ‘leaving after-effects in agreement of π’.

The breadth of a amphitheater is affected by award the aboveboard of the radius, and again adding this aftereffect by π.

Remember, you acquisition the aboveboard of a amount by adding it by itself, eg 4² = 4 x 4 = 16.

The ambit of a amphitheater is affected by adding the bore of a amphitheater by π (π × d) . The blueprint to account the ambit of a amphitheater is usually accounting c = πd.

There is an another formula, breadth you account the ambit application the ambit instead. As the bore is according to 2 × r, this blueprint is c = 2 × π × r or c = 2πr.

You can use either formula, depending on how you accept been taught.

Imagine a amphitheater that has a bore of 12 cm.

Using the formulae aloft for artful ambit (πd) and breadth (πr²), how would you account both of these, abrogation your answers in agreement of π?

The bore of the amphitheater = 12 cm

Its radius, accordingly = 6 cm

1) Ambit = πd = π × 12

Written as an acknowledgment in agreement of π = 12π cm

Circumference = 12π cm

2) Breadth = πr² = π × 6 × 6

Written as an acknowledgment in agreement of pi = 36π cm²

Area = 36π cm²

Leaving answers in agreement of π enables you to accept exact after-effects which are not rounded.

When artful the breadth or ambit of a circle, it is important every time to bifold analysis the amount that you are application for the ambit or diameter, as it can be accessible to ataxia these up.

Always bethink to accommodate units (eg cm or cm²) with all your solutions too.

Matching task

Have a go at the problems in this assignment from GCSEPod breadth you charge to bout anniversary amphitheater on the aboriginal area with the actual areas and circumferences on the additional sheet, which are all accustomed in agreement of π.

Write your answers on a allotment of paper.

Click actuality for the acknowledgment sheet.

Area and ambit of a amphitheater in agreement of π: Skills

Keep activity – now try this worksheet from GCSEPod that contains analytic questions for you to try, with a claiming at the end.

Write your answers on a allotment of paper.

Click actuality for the acknowledgment sheet.

Have a attending at these added assets about the BBC and the web.

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