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  1. The diagram represents a solid frustum with base radius of 35cm and top radius of 21cm.The frustum is 22.5cm high and is made of a metal whose density is 4g/cm3. Taking π = 22/7
    diagram representing a solid frustum
    Calculate;
    1. The volume of the metal that makes the frustum. 
    2. The mass of the frustum. 
  2. The frustum is melted in down and recast into a solid cube in the process 20% of the metal is lost. Calculate to 2d.p the length of each side of the cube.

1 Answer

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  1.  
    1.    h        = 21
      h+22.5       35
      35h = 21(h + 22.5)
      35h − 21h = 472.5
      14h − 472.5
      h = 472.5
              14
      h=33.75
      ∴ vol of frustum = 1/3π(R2H − r2h)
      1/3 × 3.14(352 × 56.25 − 212 × 33.75)
      1/3 × 3.14(68906.25 − 14883.75) 

      =56543.55cm3 
    2. Mass = D × V
      = 56543.55 × 4 = 22174.2g
  2. 80/100 × 56543.55 = 45234.84
    L×L×L = 45234.84
    =35.63cm
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