Question
A frustum of a cone has a lower base radius of 12 cm, an
upper base radius of 8 cm, and a height of 15 cm. Find the total surface area of the frustum.Solution
The slant height (l) of the frustum is given by l = √(h² + (r1 - r2)²), where h = 15 cm, r1 = 12 cm, and r2 = 8 cm. Slant height l = √(15² + (12 - 8)²) = √(225 + 16) = √241 ≈ 15.52 cm. The total surface area of the frustum = π * (r1 + r2) * l + π * (r1² + r2²). Total surface area = π * (12 + 8) * 15.52 + π * (12² + 8²). = π * 20 * 15.52 + π * (144 + 64). = 310.4π + 208π = 518.4π square cm.
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