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Volume & Surface Area of Solids

Volume & Surface Area of Solids. Basic Volumes. Volume of a Pyramid. Volume of a Sphere. www.mathsrevision.com. Composite Volume Problems. Exam Type Questions. Starter Questions. Q1. True or false. Q2. Write down the probability of picking out a number

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Volume & Surface Area of Solids

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  1. Volume & Surface Area of Solids Basic Volumes Volume of a Pyramid Volume of a Sphere www.mathsrevision.com Composite Volume Problems Exam Type Questions

  2. Starter Questions Q1. True or false Q2. Write down the probability of picking out a number greater than 20 in the national lottery. www.mathsrevision.com Q3. If a = -3 and b = -4 does a2 – 3b2 = 57 Q4. Calculate Created by Mr.Lafferty

  3. Example Find the volume of the composite shape. N5 LS VT = V1 + V2 7 cm VT = 105 + 720 5 cm VT = 825 cm3 3 cm 9 cm V1 = l x b x h www.mathsrevision.com = 3 x 5 x 7 V2 = l x b x h = 105 cm³ 10 cm = 8 x 10 x 9 8 cm = 720 cm³ Compiled by Mr. Lafferty Maths Dept.

  4. Triangle Area = 4cm 10cm 4cm Volume of a Triangular Prism Working = 2 x4 = 8 cm2 Volume = Area x length = 8 x 10 = 80cm3 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  5. Triangle Area = 6cm Example Find the volume of the triangular prism. Working = 3 x 3 = 9 cm2 Volume = Area x length = 9 x 30 = 270cm3 3cm 30cm www.mathsrevision.com Total Area = 6+6+30+40+50 = 132cm2 Compiled by Mr. Lafferty Maths Dept.

  6. Triangle Area = Example Find the volume of this prism. Working = 6 x 8 = 48 m2 Rectangle = l x b = 6 x 12 = 72cm2 8cm Total Area = 72 + 48 = 120 m2 6cm www.mathsrevision.com 15cm 12cm Volume = Area x length = 120 x 15 =1800m3 Total Area = 6+6+30+40+50 = 132cm2 Compiled by Mr. Lafferty Maths Dept.

  7. Volume of a Cylinder Example : Find the volume of the cylinder below. 5cm V = πr2h 10cm www.mathsrevision.com = π(5)2x10 Cylinder (circular Prism) = 250π cm3 = 784.5 cm3

  8. Example Find the length the cuboid This just an equation. We know how to solve them ! N5 LS 4 cm Volume = L x B x H V=200cm3 200 = L x 5 x 4 5 cm www.mathsrevision.com 200 = 20L 10 cm L 20L = 200 L = 10 Compiled by Mr. Lafferty Maths Dept.

  9. Volume Now Try TJ N5 Lifeskills Revision Ex Ch19 (page 173) www.mathsrevision.com

  10. Starter Questions 10cm Q1. Find the area of the triangle. 3cm 4cm Q2. Expand out and simplify 2w2 – 3(2w – 5) www.mathsrevision.com Q3. True or false Q4. Rearrange into the form y = 2y – 3x + 7 = 0 Created by Mr.Lafferty

  11. Volume of a Pyramid N5 LS Learning Intention Success Criteria • To know formula. • We are learning how to use the formula for the volume of ANY pyramid and apply it to solve problems. • Apply formula correctly. www.mathsrevision.com • Work backwards using formula.

  12. Volume of a Pyramid N5 LS The volume of any pyramid can be calculated using the formula www.mathsrevision.com A = Area of base h = height cone

  13. Volume of Pyramid N5 LS Q. Find the volume the pyramid. 12m 100m2 www.mathsrevision.com

  14. Volume of a Cone N5 LS h r www.mathsrevision.com • If the above cone has radius 15cm and height • of 10 cm. Calculate it’s volume.

  15. Volume Now Try TJ N5 Lifeskills Ex 19.1 Ch19 (page 174) www.mathsrevision.com

  16. Starter Questions Q1. Find the area of the triangle. 10cm 6cm Q2. Factorise 2x2 – 6x www.mathsrevision.com Q3. Calculate Created by Mr.Lafferty

  17. Volume of Solids N5 LS Learning Intention Success Criteria • To know the volume formula for a sphere. • We are learning how to use the sphere formula and use it to solve real-life problems. • Work out volumes for spheres. www.mathsrevision.com • Answer to contain • appropriate units and working.

  18. Volume of a Sphere N5 LS D = diameter r D www.mathsrevision.com Q. If the above sphere has radius 10cm. Calculate it’s volume.

  19. Volume Now Try TJ N5 Lifeskills Ex 19.2 Ch19 (page 177) www.mathsrevision.com

  20. Starter Questions • In pairs, • think of the type of volume questions • Easy • Medium • Hard www.mathsrevision.com Created by Mr.Lafferty

  21. Volume of Solids N5 LS Learning Intention Success Criteria • To know the volume formula for various basic shapes. • We are learning how to calculate composite volume of complicated shapes. • Work out volumes for composite shapes. www.mathsrevision.com • Answer to contain • appropriate units and working.

  22. r 2m Volume of a sphere N5 LS Q. Find the volume the composite shape. Volume = Cylinder + half a sphere ½ sphere Cylinder www.mathsrevision.com h = 6m

  23. Volume Now Try TJ N5 Lifeskills Ex 19.3 Ch19 (page 179) www.mathsrevision.com

  24. Part b on next slide

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