A cone of height 24\text{ cm} has a curved surface area 550\text{ cm}^2. What is the ratio of its radius to slant height? (Take \pi=\frac{22}{7})

  1. A. \frac{5}{12}
  2. B. \frac{5}{13}
  3. C. \frac{7}{25} ✓
  4. D. \frac{7}{27}

Correct Answer: C. \frac{7}{25}

Explanation

Curved Surface Area = \pi r l = 550. Slant height l = \sqrt{r^2+24^2}. Substitute \pi = \frac{22}{7} to get \frac{22}{7} r \sqrt{r^2+576} = 550 \implies r\sqrt{r^2+576} = 175. Let r = 7, then l = \sqrt{49+576} = 25, satisfying 7 \times 25 = 175. The ratio \frac{r}{l} = \frac{7}{25}.

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