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The diagram represents a solid frustum with base radius 21cm and top radius 14cm. The frustum is 22.5cm high and is made of a metal whose density is 3 g/cm3.
(Take π=22/7)
MathF4OPP1Q23

  1. Calculate
    • The volume of the metal in the frustum.
    • The mass of the frustum in kg. 
  2. The frustum is melted down and recast into a solid cube. In the process 20% of the metal is lost. Calculate to 2 decimal places the length of each side of the cube.

1 Answer

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  1.    
    • Volume
      Ratio x/14 =(22.5+x)/21
      21X=14(22.5 +X)
      21= 14(22.5 + x)
      21x - 14x = 315
      x = 45cm
      Volume of whole cone
      =1/3 x 22/7 x 21 x 21 x 67.5 =31185 cm3
      Volume of small cone
      =1/3 x 22/7 x14 x 14 x 45 = 9240 cm3 
      Volume of frustum
      31185- 9240 = 21 945 cm3
       
    • Mass of frustum
      Mass=21945x3g/cm3 =65835g 
      Mass in kg= (65.835 g)/1000g = 65835kg
       
  2. 20% of 65.835kg = 13.167 kg
    65.835 - 13.167 = 52.668 kg
    Volume of material remaining =
    56682/3= 17556cm3
    Length of cube = ∛(17 556 )= 25.99 cm
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