Chapter 1: Q42. (page 4)

Find the circumference and area of each circle. Round to nearest tenth.

Expert verified

$\begin{array}{l} Circumferenceofgivencircle C = 50.3 cm \\ Areaofgivencircle A = 201.1 {cm}^{2} \end{array}$

Step by step solution

In the given circle, observe that the diameter of the circle is 16 cm, so the radius must be half of the diameter, that is,

$\begin{array}{l} r = \frac{d}{2} \\ r = \frac{16}{2} \\ r = 8 cm \end{array}$

The circumference and area of a circle of radius r are given by.

$\begin{array}{l} Circumferenceofacircle C = 2 π r \\ Areaofacircle A = π r^{2} \end{array}$

In order to find the circumference of the circle, use the above formula and substitute 8 for r and simplify further as shown below.

$\begin{array}{l} Circumferenceofcircle \\ C = 2 π (8) \\ C = 16 π \\ C = 50.3 cm \end{array}$

In order to find the area of the circle, use the above formula and substitute 8 for r and simplify further as shown below:

$\begin{array}{l} Areaofcircle \\ A = π r^{2} \\ A = π {(8)}^{2} \\ A = 64 π \\ A = 201.1 {cm}^{2} \end{array}$

Therefore,

$\begin{array}{l} Circumferenceofgivencircle C = 50.3 cm \\ Areaofgivencircle A = 201.1 {cm}^{2} \end{array}$

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