To find the lateral surface area (A_l) of a cone, we use the formula:
\[ A_l = \pi r l \]
where \( r \) is the radius of the base and \( l \) is the slant height.
From the given dimensions:
- The height (h) of the cone is 13 meters.
- The diameter (d) of the base is 28 meters, so the radius (r) is half of the diameter:
\[ r = \frac{28}{2} = 14 \text{ meters} \]
We also need the slant height (l). From the Pythagorean theorem, the slant height (l) can be found as follows:
\[ l = \sqrt{r^2 + h^2} \]
Substituting the known values:
\[ l = \sqrt{14^2 + 13^2} = \sqrt{196 + 169} = \sqrt{365} \approx 19.10 \text{ meters} \]
Now we can substitute these values into the formula for the lateral surface area:
\[ A_l = \pi r l = \pi \times 14 \times 19.10 \approx 3.14159 \times 14 \times 19.10 \approx 841.43 \text{ square meters} \]
Given the options, it appears there was an error or misinterpretation. The closest match to the calculated latral surface area is 381.18 m² which doesn't fit, there might be mistake in calculations or options given.
11. Find the lateral surface area of the cone 13m by 28m.
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Captionless Image
381.18 m squared
1143.54 m squared
1674.47 m squared
4389 m squared
1 answer