Question One Boxed In Question Two 25cm2 12cm2

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Presentation transcript:

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.

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) = 502.7 cm3 Volume left = 5497.35cm3

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

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.

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)

Lesson Objective

Plenary