1. 1
   A stationery company is checking measurements for a batch of products: a rectangular notebook cover 18 cm by 24 cm, a circular badge of radius 3.5 cm, and a cylindrical pencil tub of radius 4 cm and height 15 cm. Use pi = 3.14 throughout.

   (a)

   What is the area of the notebook cover?

   [1 mark]

   • A216 cm^2
   • B432 cm^2
   • C84 cm^2
   • D864 cm^2

   (b)

   What is the circumference of the badge, to the nearest cm?

   [1 mark]

   • A22 cm
   • B11 cm
   • C38 cm
   • D44 cm

   (c)

   What is the volume of the pencil tub, to the nearest cm^3?

   [1 mark]

   • A377 cm^3
   • B188 cm^3
   • C1508 cm^3
   • D754 cm^3

   Total for question 1: 3 marks

2. 2
   A model railway manufacturer produces two similar model bridges. The smaller bridge is 15 cm long and has a base area of 45 cm^2. The larger bridge is 25 cm long.

   (a)

   Find the length scale factor from the smaller bridge to the larger bridge.

   [2 marks]

   (b)

   Hence find the base area of the larger bridge.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A garden sprinkler sweeps out a sector of a circular lawn with radius 8 m and sector angle 150 degrees. Use pi = 3.14.

   (a)

   Calculate the arc length of the sector, giving your answer to 1 decimal place.

   [3 marks]

   (b)

   Calculate the area of the sector, giving your answer to 1 decimal place.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A confectioner sells chocolate spheres in two similar sizes: a small sphere of radius 3 cm and a large sphere of radius 6 cm. Use pi = 3.14 throughout.

   (a)

   Show that the volume of the large sphere is 904.32 cm^3.

   [4 marks]

   (b)

   Using the volume scale factor between the two similar spheres and the volume found in part (a), calculate the volume of the small sphere.

   [4 marks]

   (c)

   Twelve small spheres are packed into a cuboid box measuring 12 cm by 18 cm by 12 cm. Calculate the volume of empty space remaining in the box after packing, giving your answer to the nearest cm^3.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   A garden centre is labelling three items: a triangular herb planter with base 40 cm and height 25 cm, a circular fountain basin of radius 1.2 m, and a cone-shaped plant pot with base radius 6 cm and perpendicular height 8 cm. Use pi = 3.14 throughout.

   (a)

   What is the area of the triangular herb planter?

   [1 mark]

   • A1000 cm^2
   • B250 cm^2
   • C500 cm^2
   • D65 cm^2

   (b)

   What is the circumference of the fountain basin, to 1 decimal place?

   [1 mark]

   • A3.8 m
   • B7.5 m
   • C4.5 m
   • D15.1 m

   (c)

   What is the volume of the plant pot, to the nearest cm^3?

   [1 mark]

   • A301 cm^3
   • B904 cm^3
   • C100 cm^3
   • D603 cm^3

   Total for question 5: 3 marks

6. 6
   A school playground is an L-shaped compound formed by a 20 m by 14 m rectangle with a 6 m by 5 m rectangular section removed from one corner.

   (a)

   Calculate the area of the playground.

   [2 marks]

   (b)

   Calculate the perimeter of the playground.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A metal water tank is a cylinder of radius 0.5 m and height 2 m, open at the top. Use pi = 3.14 throughout.

   (a)

   Calculate the volume of the tank, giving your answer to 2 significant figures.

   [3 marks]

   (b)

   Calculate the total surface area of the tank (the curved surface and the base only, since it is open at the top), giving your answer to 2 significant figures.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   A skate park is building a ramp base with a compound shape: a rectangle measuring 10 m by 6 m, with a quarter-circle of radius 6 m attached to one of the 6 m ends. The quarter-circle's arc forms the boundary of the shape in place of that end, and its two straight radii lie along the two 10 m sides of the rectangle. Use pi = 3.14 throughout.

   (a)

   Calculate the area of the compound shape, giving your answer to the nearest m^2.

   [4 marks]

   (b)

   Calculate the perimeter of the compound shape, giving your answer to the nearest metre.

   [4 marks]

   (c)

   The ramp is to be edged with a safety strip costing $12 per metre along the straight sides found in part (b), and $17 per metre along the arc (the standard rate plus a $5 per metre surcharge for the curved section). Calculate the total cost of edging the whole ramp.

   [5 marks]

   Total for question 8: 13 marks

End of questions