Question

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)

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.

Answer 1

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