Chapter 19: Review

Return to the pond

The pond has radius $4$ m. Its circumference is $2\pi r=8\pi$ m, about $25.1$ m. Its area is $\pi r^2=16\pi$ m², about $50.3$ m². The first estimate should be close to these values. A path border needs the circumference; a cover over the water needs the area.

Mixed practice

For each question, choose a method first. Say why it applies, then calculate. Check the units in your answer.

1. A room is 5 m by 3.5 m. Work out its area and perimeter.
2. A circular table has diameter 1.2 m. Work out its circumference in terms of $\pi$.
3. A $120^\circ$ sector has radius 6 cm. Work out its area in terms of $\pi$.
4. A prism has cross-section area $24\text{ cm}^2$ and length 9 cm. Work out its volume.
5. A sphere has radius 2 cm. Work out its surface area in terms of $\pi$.
6. A $10$ cm by $8$ cm rectangle has a $3$ cm by $2$ cm corner removed. Work out the remaining area.
7. A map uses a scale of 1 cm to represent 2 m. A garden border measures 7 cm on the map. Work out its real length. Which methods did you use?
8. A container holds 2.4 litres. Convert this to cubic centimetres using $1$ litre $=1000$ cm³. Explain why volume units are needed.

Reflect

Which formula can you now choose without a prompt? Which measurement still needs a labelled sketch? Note a next step for your practice.