Question

A cylindrical metal bar of diameter 14cm and length 2m is melted and moulded into spherical balls. In the process, 5% by volume of metal is lost and what remains makes balls of radius 3.5cm.

1. calculate the volume of metal used to make the balls. 
2. find to the nearest whole number the number of balls made 
3. find the total surface area of the metal bar 
4. find the total surface area of the balls made

Answer 1

1. ²²/_7 × 7 ×7 × 200 =30,800cm³  
   Remaining = ⁹⁵/₁₀₀ × 30800   
                   = 29,260cm³    
2. ⁴/₃ × ²²/₇ × 3.5³ = volume of 1 ball
   No. of balls = 29260 × 21        
                         4×22×3.53
                   =162.86               
                   =162 balls             
3. 2 × ²²/₇ × 7² =308
    C.S = 2× ²²/₇ × 7 ×200 =8800   
   T.S.A =8800 + 308
           =9108cm²                      
4. 162 × 4 × ²²/₇ × 3.5²    
                =24948cm²