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
.
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.
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