Question

12 using exact values (e.g. \\(10 + 4\pi\\)), find the area of the shapes given in question 6.

13 a circle of radius \\(10\text{ cm}\\) has a hole cut out of its centre to form a ring. find the radius of the hole if the remaining area is \\(50\\%\\) of the original area. round to one decimal place.

14 use pythagoras theorem (illustrated in this diagram) to help explain why these composite shapes include incorrect information.

a
b
c

enrichment: construction cut-outs

15 the front of a grandfather clock consists of a timber board with dimensions as shown. a circle of radius \\(20\text{ cm}\\) is cut from the board to form the clock face. find the remaining area of the timber board correct to one decimal place.

16 the number 10 is cut from a rectangular piece of paper. the dimensions of the design are shown below.

Explanation:

Calculate the original area

Using the Area of an Annulus knowledge point

$$ A_{\text{original}} = \pi R^2 = \pi (10)^2 = 100\pi $$

Set up the remaining area equation

Using the Area of an Annulus knowledge point

$$ A_{\text{remaining}} = 0.50 \times A_{\text{original}} = 50\pi $$

Relate remaining area to the inner radius

Using the Area of an Annulus knowledge point

$$
LATEXBLOCK0
$$

Solve for the inner radius

Using the Area of an Annulus knowledge point

$$
LATEXBLOCK1
$$

Answer:

A circle of radius \(10\text{ cm}\) has a hole cut out of its centre to form a ring. Find the radius of the hole if the remaining area is \(50\%\) of the original area. Round to one decimal place.
The radius of the hole is <blank>\(7.1\)</blank> \(\text{cm}\).