Measuring Space: Perimeter and Area | Exercise 6.1

Question 2

Unless stated otherwise, use the approximation 227\frac{22}{7} for π\pi.

  1. Calculate, correct to 3 significant figures, the circumference of a circle with: (i) radius 7 cm

(ii) radius 10 cm

(iii) radius 12 cm.

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Solution

We will use the formula for the circumference of a circle.

Step 1 — Calculate for radius 7 cm

First, let's look at the radius. The radius is 7 cm. We use the formula for circumference. C=2πrC = 2\pi r We substitute the values. C=2×227×7C = 2 \times \frac{22}{7} \times 7 =2×22= 2 \times 22 =44= 44 We need to give the answer to 3 significant figures.

44.0 cm\boxed{44.0 \text{ cm}}

Step 2 — Calculate for radius 10 cm

Next, let's consider the radius. The radius is 10 cm. We use the circumference formula again. C=2πrC = 2\pi r We substitute the values. C=2×227×10C = 2 \times \frac{22}{7} \times 10 =4407= \frac{440}{7} =62.85714...= 62.85714... We round this to 3 significant figures.

62.9 cm\boxed{62.9 \text{ cm}}

Step 3 — Calculate for radius 12 cm

Finally, let's use the last radius. The radius is 12 cm. We apply the circumference formula. C=2πrC = 2\pi r We substitute the values. C=2×227×12C = 2 \times \frac{22}{7} \times 12 =5287= \frac{528}{7} =75.42857...= 75.42857... We round this to 3 significant figures.

75.4 cm\boxed{75.4 \text{ cm}}

Answer

(i) 44.0 cm (ii) 62.9 cm (iii) 75.4 cm

More questions in Exercise 6.1

Q1

Unless stated otherwise, use the approximation 227\frac{22}{7} for π\pi.

  1. The perimeter of a circle is 44 cm. What is its radius?
Q2

Unless stated otherwise, use the approximation 227\frac{22}{7} for π\pi.

  1. Calculate, correct to 3 significant figures, the circumference of a circle with: (i) radius 7 cm

(ii) radius 10 cm

(iii) radius 12 cm.

Q3

Unless stated otherwise, use the approximation 227\frac{22}{7} for π\pi.

  1. Calculate the length of the arc of a circle if:

(i) the radius is 3.5 cm3.5\text{ cm} and the angle at the centre is 60∘60^\circ, and

(ii) the radius is 6.3 m6.3\text{ m} and the angle at the centre is 120∘120^\circ.

Q4

Unless stated otherwise, use the approximation 227\frac{22}{7} for π\pi.

  1. Find the perimeter of a sector (i.e., the curved portion as well as the two straight portions) of a circle of radius 14 cm and sector angle 75°.
Q5

Unless stated otherwise, use the approximation 227\frac{22}{7} for π\pi.

  1. Find the perimeters of the following shapes (taking the arcs to be quarter or half or three-quarters of a circle, as appropriate) (Fig. 6.14i to 6.14ix):
Q6

If the diameter of a car tyre is 56 cm, then:

(i) How far does the car need to travel for the tyre to complete one revolution?

(ii) How many revolutions does the tyre make if the car travels 10 km?

Q7

Find the total perimeter of all the petals in each of the given flowers.

Q8

The ratio of the perimeters of two circles is 5:4. What is the ratio of their radii?

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