1. Question One Boxed In Question Two 25cm2 12cm2
The diagram shows a rectangular box.
The areas of the faces are 3, 12 and 25 square centimetres.
What is the volume of the box?
Boxed In
3cm2
25cm2
12cm2
Question Two
A Solid cube has a square hole cut through horizontally and a circular hole cut through vertically. Both holes are central.
Calculate the volume remaining after the holes have been cut.

2. Circular holes = 2 (pie × 42 × 5) = 502.7 cm3
Answers
Question One
l = 2.5cm, w = 1.2cm, h = 10cm, volume = 30cm3
Question Two
Volume cube = 203 = 8000 cm3
Square hole = 102 × 20 = 2000 cm3
Circular holes = 2 (pie × 42 × 5) = cm3
Volume left = cm3

3. Task Using the piece of card Make a net of a cylinder
Make sure it is accurate so it fits together perfectly
Do not worry about making tabs
Once you have done this
Find the total surface area

5. Volume of a cylinder
A cylinder is a special type of prism with a circular cross-section.
Remember, the volume of a prism can be found by multiplying the area of the cross-section by the height of the prism. h r
The volume of a cylinder is given by:
V = πr2h
Volume = area of circular base × height or
Recall that the area of a circle is equal to πr2.

6. Surface area of a cylinder
To find the formula for the surface area of a cylinder we can draw its net.
How can we find the width of the curved face? r
The width of the curved face is equal to the circumference of the circular base, 2πr.
2πr ? h
Area of curved face = 2πrh
Discuss the factorization 2πrh + 2πr2 = 2πr(h + r).
If pupils are familiar with dimensions, you could ask them to check that this formula is correct dimensionally.
Area of 2 circular faces = 2 × πr2
Surface area of a cylinder = 2πrh + 2πr2 or
Surface area = 2πr(h + r)

7. Lesson Objective

8. Plenary