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GCSE: Volumes and Surface Area

GCSE: Volumes and Surface Area. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: 7 th December 2013. All the GCSE formulae for 3D shapes. (The * indicates ones that won’t be in your formula booklet). r. r. l. h. r. ?. ?. ?. ?. ?. *. Area of curved surface .

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GCSE: Volumes and Surface Area

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  1. GCSE: Volumes and Surface Area Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 7th December 2013

  2. All the GCSE formulae for 3D shapes (The * indicates ones that won’t be in your formula booklet) r r l h r ? ? ? ? ? * Area of curved surface Bro Tip: ‘Roll out’ the cylinder to work out the area of the curved surface. ? ? * h Bro Tip: The same formula applies to the cone.

  3. Hemispheres Give your answers in terms of . Volume = ? 3cm ? Surface Area = For a Sphere: ? ?

  4. Quickfire Examples 2m 10m ? ? ? ?

  5. Hemisphere Exercises Find the formula of these solid shapes, in terms of p unless where specified. (Copy out the shape first) 1 2 Mr Wutang and his clan eat from a full bowl of rice, a bowl with diameter 18cm. He eats 400g. What is the density of the rice to 3sf? (in g/cm3) Volume = 486 Density = 400 / 486 = 0.262g/cm3 3 42m 6 ? Volume = 6174 m3 Surface Area = 1764 m2 Volume = 288 Surface Area = 108 ? ? ? ? 4 18cm 5 What radius is needed for a hemisphere so that the volume is 18m3? 6cm A hemispherical bowl with radius 18cm, with a rim of width 6cm. Volume = 3888 – 1152 = 2736 Surface Area = 1296 + 324 – 144 = 1476 ? ? ?

  6. Frustum A frustum is a cone with part of the top chopped off. 2 1 Volume = ? 12 8 9 4 12 Your Go... Volume ? (Hint: you’ll need to work out the radius of the top circle, perhaps by similar triangles?) For a Cone:

  7. Surface Area of Cones ? 4 ? ? 3 Area of curved surface (where l is the slant height)

  8. Exercises 1 2 Volume = 100 Surface Area = 90 ? Volume = 96 Surface Area = 96 ? ? ? 12 8 5 4 3 3 12 12 Surface Area ?

  9. A* Question √50 5√2 Length of bottom diagonal = 10√2 (by Pythagoras) Height of pyramid = √ 50 (again by Pythagoras) Volume = 1/3 x √50 x 102 = 236cm3 ? ? ?

  10. Melting 3km Darth Vader decides he doesn’t like the shape of his Death Star, so melts it down and rebuilds it using the same amount of material to form a Death Cube. What is the side length x of his Death Cube? ?

  11. Melting x 4r 3r x 3x 5y ? What is r in terms of x? 4y 2x ?

  12. Questions on Provided Sheet ?

  13. Questions on Provided Sheet 6 x 10 x 8 = 6 x 20 x d 80 = 20d d = 4cm ?

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