Question

5 what is the area of an annulus with circles of radii 17 cm and 8.5 cm? answer in square centimetres correct to one decimal place.

6 an annulus consists of two circles with the same centre. find the area of an annulus that has an inner diameter of 6 cm and an outer diameter of 10 cm. answer correct to the nearest square centimetre.

Explanation:

Identify given values and formulas

We need to find the area of an annulus for two separate questions. An annulus is the region between two concentric circles.
The formula for the area of an annulus is:

$$A = \pi R^2 - \pi r^2 = \pi (R^2 - r^2)$$

where \(R\) is the outer radius and \(r\) is the inner radius.

Solve Question 5

For Question 5, the given radii are:

• Outer radius \(R = 17\text{ cm}\)
• Inner radius \(r = 8.5\text{ cm}\)

Calculate the area:

$$A = \pi (17^2 - 8.5^2)$$

$$A = \pi (289 - 72.25)$$

$$A = 216.75\pi \approx 680.94\text{ cm}^2$$

Rounding to one decimal place gives \(680.9\text{ cm}^2\).

Solve Question 6

For Question 6, the given diameters are:

• Inner diameter = \(6\text{ cm}\) \(

ightarrow\) Inner radius \(r = 3\text{ cm}\)

• Outer diameter = \(10\text{ cm}\) \(

ightarrow\) Outer radius \(R = 5\text{ cm}\)

Calculate the area:

$$A = \pi (5^2 - 3^2)$$

$$A = \pi (25 - 9)$$

$$A = 16\pi \approx 50.27\text{ cm}^2$$

Rounding to the nearest square centimetre gives \(50\text{ cm}^2\).

Answer:

Question 5

\(680.9\text{ cm}^2\)

Question 6

\(50\text{ cm}^2\)