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Calculating Volume and Surface Area of a Cylinder: Geometry Task

Solve volume and surface area problems of a rectangular box and a cube with holes using formulas and calculations. Create a net of a cylinder accurately, find total surface area, and understand cylindrical geometry concepts.

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Calculating Volume and Surface Area of a Cylinder: Geometry Task

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  1. 25cm2 12cm2 3cm2 Question One 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 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. Answers • Question One • l = 2.5cm, w = 1.2cm, h = 10cm, volume = 30cm3 • QuestionTwo Volume cube = 203 = 8000 cm3 Square hole = 102 × 20 = 2000 cm3 Circular holes = 2 (pie × 42 × 5) = 502.7 cm3 Volume left = 5497.35cm3

  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

  4. Volume of a cylinder r Volume = area of circular base × height h or V = πr2h 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. The volume of a cylinder is given by:

  5. Surface area of a cylinder Surface area = 2πr(h + r) or 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 Area of 2 circular faces = 2 × πr2 Surface area of a cylinder = 2πrh +2πr2

  6. Lesson Objective

  7. Plenary

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