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Question
If R is the radius of the base of the hat, then the total outer surface area of the hat is ______.
Options
πr(2h + R)
2πr(h + R)
2πrh + πR2
None of these
Solution
If R is the radius of the base of the hat, then the total outer surface area of the hat is 2πrh + πR2.
Explanation:
Given, a cylindrical hat with base radius R and r is the radius of the top surface.
Now, total surface area of hat = Curved surface area + Top surface area + Base surface area
= 2πrh + πr2 + π(R2 – r2)
= 2πrh + πr2 + πR2 – πr2
= 2πrh + πR2
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