The height of a solid cylinder is 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm2) of the remaining solid?
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$430π$
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$120π$
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$230π$
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$433π$
A
Correct answer
Explanation
Original cylinder: radius = 5 cm, height = 30 cm. Curved surface area = 2πrh = 2π × 5 × 30 = 300π. Each conical hole: slant height = √(5²+12²) = 13 cm. Curved surface of each cone = πrl = π × 5 × 13 = 65π. Final surface area = curved cylinder + 2 × base area - 2 × conical surface = 300π + 2π(5)² - 2(65π) = 300π + 50π - 130π = 220π. Wait - this doesn't match. Let me reconsider: when holes are drilled, we lose the base circles but gain the conical surfaces. Correct: 300π (cylinder CSA) + 50π (top base) - 2×25π (bottom base holes removed) + 2×65π (conical surfaces) = 430π.