2021 · Q38
A cone of height 24 cm has a curved surface area 550 cm². What is the ratio of its radius to slant height? (Take π = 22/7)
Elementary MathematicsMensuration
- A5/12
- B5/13
- C7/25
- D7/27
Explanation
πrl = 550 gives rl = 175 (with π = 22/7). Since l² = r² + 24² = r² + 576, we get r²(r²+576) = 175² = 30625. Solving u² + 576u − 30625 = 0 with u = r² gives u = 49. So r = 7, l = 175/7 = 25, and r : l = 7 : 25. Hence option C.