A solid metal cylinder of 12 cm height and 7 cm radius

Solution

Volume of Cylinder = πr²h = π × 7² × 12 = 588π Now, the solid metal cylinder is re-cast into two cones in the proportion 1: 2 i.e. the volumes of cone 1 and cone 2 is 196 π and 392 π respectively. So, flat Surface area of cylinder before melting = 2πr² = 2 × 7² = 98π   Volume of cone 1 =1/3 πr1²h= 196π   r1² = (196×3/ 12) = 49 Volume of cone 2 = 1/3πr2²h = 392π   r2² = 392×3 /12 = 98 Flat surface area of cones = π (r1² + r2²⁾ = π (49 + 98) = 147π   Percentage change in surface area = (147-98π) /98π × 100 = 1/2 × 100 = 50%