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  1. 9Similar triangles, shadows
  2. 10Similar triangles, area ratio
  3. 1230-60-90 triangle sides
  4. 14Angle of elevation, right triangle
  5. 18Inscribed angle theorem
  6. 19Angle in a semicircle
  7. 21Equal tangent lengths
  8. 22Chord distance from centre
  9. 26Interior angles of an octagon
  10. 30Area and side of a rhombus
  11. 31Prism volume and surface area
  12. 33Volume and slant height of cone
  13. 40Perpendicular bisector
  14. 41Area of triangle by coords
  15. 42Circle, completing the square

33Volume and slant height of cone

A cone has base radius 6 cm and height 8 cm. Find its volume and its slant height. Give the answer to 2 decimal places.

The volume is ⅓πr²h = ⅓π(6²)(8) = 96π ≈ 301.59 cm³, and the slant height comes from Pythagoras on the radius and height: √(6²+8²) = √100 = 10.00 cm. Check: 6²+8² = 100 = 10².

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