A solid metal cylinder of 10 cm height and 14 cm diameter is melted and re-cast into two cones in the proportion of 3 : 4 (volume), keeping the height 10 cm. What would be the percentage change in the flat surface area before and after?
Explanation:
Flat surface area of the cylinder = 2 × π × 72 = 98 π cm2 Volume of the cylinder = π × 72 ×10 = 490 π cm3 Volume of cone A = (3/7) × 490 π = 210 π cm3 = (1/3) × flat surface area of cone A × 10 Flat surface area of cone A = 63 π cm2 Volume of cone B = (4/7) × 490 π = 280 π cm3 = (1/3) × flat surface area of cone B × 10 Flat surface area of cone B = 84 π cm2 Total flat surface area of cones = (63 + 84) π = 147 π cm2 Percentage change in the flat surface area = (147 – 98)/98 × 100 = 50% Hence, option (d).
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