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Question

Find the surface area of a conical hat, if its slant height is three times the radius and the base diameter of a hat is 4 inches. (Use π=3).

A
48 in2
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B
36 in2
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C
48 in
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D
46 in2
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Solution

The correct option is B 36 in2
We know, the total surface area of a cone is A=πr(r+l).

But since it a hat, therefore, we will have to subtract the circular area because the hat is not completely covered with a circular part.

Here, the diameter is 4 inch and therefore, the radius is half of diameter that is r=2 inch and it is also given that slant height is thrice the radius that is l=(3×2)=6 inch. We use π=3.

Thus,
Area of hat=πr(r+l)πr2=3×2(2+6)3×2×2=3×2×812=36 in2.

Hence, the surface area of the conical hat is 36 in2.

Therefore, option B is correct.

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