Mixed Review
These questions combine conversions, perimeter, area, circles, volume, density, similarity and composite solids.
Part A: Core Skills
- Convert 3.6 m² to cm².
- Find perimeter of a rectangle 14 cm by 9 cm.
- Find area of a triangle with base 18 cm and height 7 cm.
- Find circumference of a circle of diameter 12 cm.
- Find volume of a cuboid 8 cm by 5 cm by 3 cm.
Part B: Solids and Scale
- Find total surface area of a cube side 7 cm.
- Find volume of a cylinder radius 4 cm, height 9 cm.
- Two similar solids have linear scale factor 3. Smaller volume is 24 cm³. Find larger volume.
- A substance has mass 2.4 kg and volume 300 cm³. Find density in g/cm³.
Part C: Application
- A circular garden has radius 5 m and is surrounded by a path 2 m wide. Find path area.
- A cone of radius 6 cm and height 12 cm is attached to a cylinder of the same radius and height 8 cm. Find total volume.
- A 1:100 plan shows a rectangular room 6.5 cm by 4 cm. Find real floor area.
✅ Check Your Work
Show mixed review answers
- 36,000 cm².
- 46 cm.
- 63 cm².
- 12π≈37.7 cm.
- 120 cm³.
- 294 cm².
- 144π≈452.4 cm³.
- 24×27=648 cm³.
- 2400 g÷300=8 g/cm³.
- Outer radius=7; path area=π(49−25)=24π≈75.4 m².
- Cylinder=288π; cone=144π; total=432π≈1357.2 cm³.
- Actual dimensions 6.5 m by 4 m; area=26 m².
Reflection
- Can you choose the correct formula without being told?
- Can you keep units consistent?
- Can you split composite objects into familiar parts?
- Can you explain why your answer is reasonable?
Revision Guidance and Readiness
- Attempt the questions without notes first.
- Use the answers or worked solutions to identify the exact step that needs attention.
- Return to the relevant lesson, then retry missed questions.
- You are ready to move on when you can explain your method and check your result independently.