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ind the approximate curved surface area of a conical tent of radius 11 mm and height 2

Question

Find the approximate curved surface area of a conical tent of radius 11 mm and height 2 mm.

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Solution

To find the curved surface area of a conical tent, we use the formula:

CSA = πrℓ

where r is the radius and ℓ is the slant height of the cone.

However, in this case, we are given the radius (r = 11 mm) and the height (h = 2 mm), not the slant height. We can find the slant height using the Pythagorean theorem, since a cone is essentially a right triangle when unrolled.

The Pythagorean theorem is:

ℓ = √(r² + h²)

Substituting the given values:

ℓ = √((11 mm)² + (2 mm)²) = √(121 mm² + 4 mm²) = √125 mm = 11.18 mm

Now we can find the curved surface area:

CSA = π * 11 mm * 11.18 mm = 387.68 mm²

So, the approximate curved surface area of the conical tent is 387.68 mm².

This problem has been solved

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