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

Answer 1

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