Unit 1 Topic 2 Review — Shape and Measurement

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Review Questions

1. Q1 — Unit conversions

   Fluency

   Convert each of the following:

   (a) 3.6 km to m

   (b) 580 mm² to cm²

   (c) 4500 mL to L

   (d) 2.3 t to kg

2. Q2 — Area of shapes

   Fluency

   (a) Trapezium with parallel sides 8 cm and 14 cm, height 5 cm.

   (b) Circle with diameter 18 cm.

   (c) Sector with r = 10 cm and θ = 60°.

3. Q3 — Perimeter of composite shape

   Fluency

   A composite shape consists of a rectangle 12 cm × 7 cm with a semicircle removed from one short end (the short end has length 7 cm, so the semicircle has diameter 7 cm and radius 3.5 cm). Find the perimeter of the remaining shape.

4. Q4 — Surface area of a cylinder

   Fluency

   Find the total surface area of a closed cylinder with r = 6 cm and h = 14 cm.

5. Q5 — Volume of a cone

   Fluency

   Find the volume of a cone with r = 4 cm and h = 9 cm.

6. Q6 — L-shaped floor: area and tiling cost

   Understanding

   An L-shaped floor has outer dimensions 10 m × 8 m with a 3 m × 3 m square cut from one corner.

   (a) Find the area of the floor.

   (b) Find the cost to tile at $38 per m².

7. Q7 — Surface area and painting cost

   Understanding

   A rectangular prism has dimensions 15 cm × 8 cm × 6 cm. All outer surfaces are to be painted at $0.05 per cm². Find the surface area and total cost.

8. Q8 — Grain silo volume and capacity

   Understanding

   A grain silo consists of a cylinder (r = 2 m, h = 5 m) topped by a cone (r = 2 m, h = 3 m). Find the total volume and total capacity in kL.

9. Q9 — Similar triangles: scale factor, perimeter, area

   Understanding

   Two similar triangles: the small triangle has sides 6 cm, 8 cm, and 10 cm. The large triangle has a longest side of 25 cm.

   (a) Find the scale factor.

   (b) Find the perimeter of the large triangle.

   (c) Find the ratio of their areas.

10. Q10 — Circular lawn: radius, area, and fertiliser cost

    Understanding

    A circular lawn has a circumference of 62.8 m.

    (a) Find the radius (use π ≈ 3.14).

    (b) Find the area.

    (c) Find the cost to fertilise at $3.50 per m².

11. Q11 — Fish tank volume and capacity

    Understanding

    A rectangular fish tank measures 90 cm × 40 cm × 45 cm.

    (a) Find the volume in cm³.

    (b) Find the capacity in litres.

    (c) If filled to 80%, how many litres does it contain?

12. Q12 — Cone: find height, slant height, and TSA

    Problem Solving

    A cone has volume 452.4 cm³ and radius 6 cm.

    (a) Find the perpendicular height.

    (b) Find the slant height.

    (c) Find the total surface area.

13. Q13 — Painting a sphere

    Problem Solving

    A sphere has diameter 2 m. Paint covers 6 m² per litre and is sold in 500 mL tins for $18 each.

    (a) Find the surface area.

    (b) Find the litres of paint needed.

    (c) Find the number of 500 mL tins needed (round up).

    (d) Find the total cost.

14. Q14 — Similar cylinders: scale factor and volume

    Problem Solving

    Two similar cylinders: the small has r = 3 cm, h = 4 cm. The large has r = 7.5 cm.

    (a) Find the scale factor (small to large).

    (b) Find the height of the large cylinder.

    (c) Find the ratio of their volumes.

    (d) If the small cylinder has volume 113.1 cm³, find the volume of the large cylinder.

15. Q15 — Variable-depth swimming pool

    Problem Solving

    A swimming pool is 20 m × 10 m. The depth varies uniformly from 1 m at the shallow end to 3 m at the deep end (the cross-section, viewed from the side, forms a trapezium).

    (a) Find the cross-sectional area (trapezium: parallel sides 1 m and 3 m, width 20 m).

    (b) Find the total volume in m³.

    (c) Find the capacity in kL.

    (d) If water is pumped in at 150 L per minute, how long (in hours) does it take to fill?