Question
A solid metal cylinder of 12 cm height and 7 cm radius
is melted and recast into two cones in the proportion of 1:2 (volume), keeping the height 12 cm. What would be the percentage change in the flat surface area before and after [use π =22/7]?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%
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