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Calculating the volume of a solid

Calculating the volume of a solid. Sphere, cone and pyramid. Formula, rounding and units. Example: Find the area of a circle with radius 6∙2 cm to 3 significant figures . A = π × r 2 = π × 6∙2 2 = 120∙762 …. = 121 cm 2. You must show the formula you are using

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Calculating the volume of a solid

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  1. Calculating the volume of a solid Sphere, cone and pyramid

  2. Formula, rounding and units Example: Find the area of a circle with radius 6∙2 cm to 3 significant figures. A = π × r2 = π × 6∙22 = 120∙762 …. = 121 cm2 • You must show • the formula you are using • The substituted values • The answer prior to rounding • Rounded final answer • the units

  3. Reminders - Formulae Area of a Square Area of a Rectangle Area of a Triangle Area of a Circle Volume of a Cube Volume of a Cuboid Volume of a prism

  4. Reminder – Pythagoras’ Theorem Pythagoras’ theorem states that a2 = a Example: Calculate the height of this triangle with sides 4 cm and a base of 6 cm to 2 significant figures. b c a2 = b2 + c2 b2 = a2 - c2 h2= h = 4 cm h cm 6 cm Note: Never round until you have answered the question

  5. r Calculating the volume of a sphere Example: Calculate the volume of this football which has a diameter of 30cm D = 30cm r = V = πr3 V = Example: Calculate the volume of a hemisphere of radius 12 cm to 3 significant figures.(A hemisphere is half a sphere) V = πr3 ½ V =

  6. Calculating the volume of a cone A circular based pyramid is called a Volume = x area of circle x height So Example: Calculate the volume of this cone to 2 significant figures V = πr2h

  7. Calculating the volume of a pyramid Volume (pyramid) = 1/3 x area (of base) x height A x h Example: Calculate the volume of the statue, with a square base of 9 cm and a height of 12 cm. V = Ah

  8. Calculating the volume of a solid Sphere, cone and pyramid

  9. Formula, rounding and units Example: Find the area of a circle with radius 6∙2 cm to 3 significant figures. A = π × r2 = π × 6∙22 = 120∙762 …. = 121 cm2 • You must show • the formula you are using • The substituted values • The answer prior to rounding • Rounded final answer • the units

  10. Reminders - Formulae Area of a Square A = l2 Area of a Rectangle A = l × b Area of a Triangle A = ½ × b × h Area of a Circle A = π r2 Volume of a Cube V = l3 Volume of a Cuboid V = l × b × h Volume of a prismV = face× h

  11. Reminder – Pythagoras’ Theorem Pythagoras’ theorem states that a2 = b2 + c2 a Example: Calculate the height of this triangle with sides 4 cm and a base of 6 cm to 2 significant figures. b c a2 = b2 + c2 b2 = a2 - c2 h2 = 42 – 32 = 7 h = √7 = 2.648… = 2.6 cm 4 cm h cm 6 cm Note: Never round until you have answered the question

  12. r Calculating the volume of a sphere Example: Calculate the volume of this football which has a diameter of 30cm D = 30cm r = 15cm V = πr3 V = x π x 153 = 14137.17… = 14137 cm3 Example: Calculate the volume of a hemisphere of radius 12 cm to 3 significant figures.(A hemisphere is half a sphere) V = πr3 ½ V = 7238.23 ÷ 2 = π x 123 = 3619.11… = 7238.23… = 3620 cm3 = 7240 cm3

  13. Calculating the volume of a cone cone A circular based pyramid is called a Volume = x area of circle x height So Example: Calculate the volume of this cone to 2 significant figures V = πr2h = π x 152 x 12 = 2827.433… = 2800 cm3

  14. Calculating the volume of a pyramid Volume (pyramid) = 1/3 x area (of base) x height A x h Example: Calculate the volume of the statue, with a square base of 9 cm and a height of 12 cm. V = Ah = x 9² x 12 = x 81 x 12 = 324 cm3

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