1. 1
   A rectangular garden measures 12 m by 8 m. A circular pond of radius 3 m is positioned entirely within the garden.

   (a)

   What is the area of the garden?

   [1 mark]

   • A40 m²
   • B96 m²
   • C20 m²
   • D84 m²

   (b)

   What is the area of the pond, in terms of $\pi$?

   [1 mark]

   • A$3\pi$ m²
   • B$6\pi$ m²
   • C$9\pi$ m²
   • D$18\pi$ m²

   (c)

   What is the remaining area of the garden not covered by the pond, in terms of $\pi$?

   [1 mark]

   • A$96+9\pi$ m²
   • B$96-3\pi$ m²
   • C$87-9\pi$ m²
   • D$96-9\pi$ m²

   Total for question 1: 3 marks

2. 2
   A cylindrical water butt has radius 0.5 m and height 1.2 m.

   (a)

   Calculate the volume of the water butt, in terms of $\pi$.

   [2 marks]

   (b)

   Taking $\pi = 3.14$, calculate the volume to 2 decimal places.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A circular pizza has radius 14 cm. A slice is cut out, forming a sector with an angle at the centre of 60°.

   (a)

   Calculate the arc length of the slice, in terms of $\pi$.

   [3 marks]

   (b)

   Calculate the area of the slice, in terms of $\pi$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A garden shed is in the shape of a cuboid measuring 4 m by 3 m by 2.5 m, with a triangular prism roof on top. The roof has a triangular cross-section with base 3 m and height 1 m, and the shed is 4 m long.

   (a)

   Calculate the volume of the cuboid part of the shed.

   [4 marks]

   (b)

   Calculate the volume of the triangular prism roof.

   [4 marks]

   (c)

   The two sloped rectangular roof faces need to be painted. Each sloped face has length 4 m and width equal to the slant length of the triangular cross-section, found using Pythagoras' theorem with a horizontal half-base of 1.5 m and a vertical height of 1 m. One litre of paint covers 12 m². Calculate the minimum number of whole litres of paint needed to paint both sloped faces.

   [5 marks]

   Total for question 4: 13 marks

End of questions