Unless stated otherwise, use the approximation for . 2. Calculate, correct to 3 significant figures, the circumference of a circle with: (i) radius 7 cm (ii) radius 10 cm (iii) radius 12 cm.

Understand the Question The circumference of a circle of radius is given by the formula: We are given . For each given radius, we substitute the value into the formula and express the final result correct to 3 significant figures. Part (i) radius Step 1 · Calculate Circumference for Given radius . Using the circumference formula: Substitute the values: Correct to significant figures, . Answer > (i) Part (ii) radius Step 1 · Calculate Circumference for Given radius . Using the circumference formula: Substitute the values: Rounding to significant figures gives . Answer > (ii) Part (iii) radius Step 1 · Calculate Circumference for Given radius . Using the circumference formula: Substitute the values: Rounding to significant figures gives . Answer > (iii) Common Mistakes Significant Figures Trap: Writing instead of . An exact integer needs the trailing to explicitly show significant figures. Formula Confusion: Mistakenly using the area formula instead of the circumference formula . Rounding Errors: Truncating decimals rather than proper rounding (e.g., writing instead of rounding up to ).

Measuring Space: Perimeter and Area | Exercise 6.1

Question 2

Unless stated otherwise, use the approximation $\dfrac{22}{7}$ for $\pi$ .

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

(ii) radius 10 cm

(iii) radius 12 cm.

Solution

Understand the Question

The circumference of a circle of radius $r$ is given by the formula: $C = 2\pi r$
We are given $\pi \approx \dfrac{22}{7}$ .
For each given radius, we substitute the value into the formula and express the final result correct to 3 significant figures.

(i) radius $7\text{ cm}$

Step 1 · Calculate Circumference for $r = 7\text{ cm}$

Given radius $r = 7\text{ cm}$ .

Using the circumference formula: $C = 2\pi r$

Substitute the values:

\begin{aligned} C &= 2 \times \dfrac{22}{7} \times 7 \\[0.6em] &= 2 \times 22 \\[0.6em] &= 44 \end{aligned}

Correct to $3$ significant figures, $44 = 44.0\text{ cm}$ .

Answer

(i) $44.0\text{ cm}$

(ii) radius $10\text{ cm}$

Step 1 · Calculate Circumference for $r = 10\text{ cm}$

Given radius $r = 10\text{ cm}$ .

Using the circumference formula: $C = 2\pi r$

Substitute the values:

\begin{aligned} C &= 2 \times \dfrac{22}{7} \times 10 \\[0.6em] &= \dfrac{440}{7} \\[0.6em] &= 62.85714\dots \end{aligned}

Rounding to $3$ significant figures gives $62.9\text{ cm}$ .

Answer

(ii) $62.9\text{ cm}$

(iii) radius $12\text{ cm}$

Step 1 · Calculate Circumference for $r = 12\text{ cm}$

Given radius $r = 12\text{ cm}$ .

Using the circumference formula: $C = 2\pi r$

Substitute the values:

\begin{aligned} C &= 2 \times \dfrac{22}{7} \times 12 \\[0.6em] &= \dfrac{528}{7} \\[0.6em] &= 75.42857\dots \end{aligned}

Rounding to $3$ significant figures gives $75.4\text{ cm}$ .

Answer

(iii) $75.4\text{ cm}$

Common Mistakes

Significant Figures Trap: Writing $44\text{ cm}$ instead of $44.0\text{ cm}$ . An exact integer needs the trailing $.0$ to explicitly show $3$ significant figures.
Formula Confusion: Mistakenly using the area formula $A = \pi r^2$ instead of the circumference formula $C = 2\pi r$ .
Rounding Errors: Truncating decimals rather than proper rounding (e.g., writing $62.8\text{ cm}$ instead of rounding up to $62.9\text{ cm}$ ).

Question 2

More questions in Exercise 6.1