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Measuring Space: Perimeter and Area - Perimeter of a Circle — The C/D Ratio

Grade 9CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The perimeter of a circle is specifically referred to as its Circumference. It represents the distance around the boundary of the circle.

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For every circle, the ratio of the circumference CC to its diameter dd is a constant value. This ratio is denoted by the Greek letter π\pi (pi).

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The relationship is expressed as Cd=π\frac{C}{d} = \pi. This means the circumference is always π\pi times the diameter: C=πdC = \pi d.

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Since the diameter dd is equal to twice the radius rr (d=2rd = 2r), the formula for the circumference is also given by C=2πrC = 2\pi r.

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π\pi is an irrational number, which means its decimal representation is non-terminating and non-recurring. For practical calculations, we use approximations like π≈227\pi \approx \frac{22}{7} or π≈3.14\pi \approx 3.14.

📐Formulae

C=πdC = \pi d

C=2πrC = 2\pi r

d=2rd = 2r

π=Cd\pi = \frac{C}{d}

π≈227≈3.14\pi \approx \frac{22}{7} \approx 3.14

💡Examples

Problem 1:

A circular wire has a radius of 14 cm14\text{ cm}. Find the circumference of the wire. (Take π=227\pi = \frac{22}{7})

Solution:

Given: Radius r=14 cmr = 14\text{ cm}. Using the formula for circumference: C=2πrC = 2\pi r C=2×227×14C = 2 \times \frac{22}{7} \times 14 C=2×22×2C = 2 \times 22 \times 2 C=88 cmC = 88\text{ cm}

Explanation:

To find the circumference, we substitute the given radius into the formula C=2πrC = 2\pi r and simplify the fraction.

Problem 2:

The circumference of a circular plot is 132 m132\text{ m}. Find its diameter. (Take π=227\pi = \frac{22}{7})

Solution:

Given: Circumference C=132 mC = 132\text{ m}. Using the formula C=πdC = \pi d: 132=227×d132 = \frac{22}{7} \times d To solve for dd, rearrange the equation: d=132×722d = 132 \times \frac{7}{22} d=6×7d = 6 \times 7 d=42 md = 42\text{ m}

Explanation:

Since we need the diameter, we use the formula C=πdC = \pi d. By substituting the known circumference and π\pi, we can isolate dd to find its value.

Problem 3:

A wheel has a diameter of 70 cm70\text{ cm}. How many meters will it cover in 100100 revolutions?

Solution:

Given: Diameter d=70 cmd = 70\text{ cm}. Distance covered in 11 revolution = Circumference CC. C=πd=227×70=220 cmC = \pi d = \frac{22}{7} \times 70 = 220\text{ cm} Distance covered in 100100 revolutions: Dtotal=100×220=22000 cmD_{total} = 100 \times 220 = 22000\text{ cm} Converting to meters: 22000 cm=22000100=220 m22000\text{ cm} = \frac{22000}{100} = 220\text{ m}

Explanation:

One complete revolution of a wheel covers a distance equal to its circumference. We calculate the circumference and then multiply by the number of revolutions, finally converting the units from cm to m.