Question

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
   
   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.

Answer 1

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 = ¹/₃^π(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