Area, Surface Area and Volume: Question 5

Worked solution

Part (a): Area of the pond

The pond is a circle, so its area is $A = \pi r^{2}.$

First find the radius from the diameter. The radius is half the diameter: $r = \frac{d}{2} = \frac{14}{2} = 7\ \text{m}.$

Now substitute $r = 7$ into the area formula: $A = \pi r^{2} = \pi \times 7^{2} = \pi \times 49.$

The question asks for the answer in terms of $\pi$, so leave the $\pi$ in the answer rather than multiplying it out: $\boxed{A = 49\pi\ \text{m}^2}$

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Part (b): Circumference of the pond

The circumference of a circle can be found from either $C = 2\pi r \qquad \text{or} \qquad C = \pi d.$

Because we already have the diameter $d = 14\text{ m}$, using $C = \pi d$ is quickest: $C = \pi d = \pi \times 14 = 14\pi\ \text{m}.$

Now convert to a decimal, using the $\pi$ button on the calculator: $C = 14 \times 3.14159\ldots = 43.982\ldots\ \text{m}.$

The question asks for the answer correct to 3 significant figures. The first three significant figures are $4$, $3$ and $9$; the next digit is $8$, so we round the $9$ up, which carries over: $43.982\ldots \to 44.0\ \text{m}.$

$\boxed{C \approx 44.0\ \text{m} \ (3\text{ s.f.})}$

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Quick check

Using $C = 2\pi r$ instead gives the same result: $2 \times \pi \times 7 = 14\pi\ \text{m}$, confirming the circumference. Note how one answer is left exact ($49\pi$) while the other is given as a rounded decimal ($44.0$); always read the instruction at the end of each part to see which form is required.