### Video Transcript

Find the total surface area of a quarter sphere of radius two centimeters. Round your answer to two decimal places.

In this example, weβre looking for the total surface area of a quarter sphere, where the radius is two centimeters. We know that the outer surface area of a whole sphere with radius π is given by four π times π squared. The outer surface area of a quarter sphere, which weβll call π΄ π, is then one-quarter of this, which is π times π squared.

Now recalling that the area of a circle is also given by π times π squared, then the area of a semicircle must be half this. So thatβs ππ squared over two. And noting that the surface of a quarter sphere comprises its outer quarter spherical shell and two semicircles, where the outer shell and the two semicircles all have the same radius, we have the surface area of the quarter sphere, which weβll call π π, is π times π squared, the outer shell, plus two times ππ squared over two. Thatβs the two semicircles. This is ππ squared plus ππ squared, which is two times π times π squared.

In our case, the radius of all three elements is equal to two, so we have two times π times two squared. And thatβs equal to eight π. Eight π evaluates to 25.1327 and so on. And weβre asked to round our answer to two decimal places. The radius is given in centimeters. So our units of area will be square centimeters.

Hence, the total surface area of the quarter sphere of radius two, to two decimal places, is 25.13 square centimeters.