CK-12 Geometry - Second Edition

11.6. Surface Area and Volume of Spheres http://www.ck12.org

Solution: This is a hemisphere. Be careful when finding the surface area of a hemisphere because you need to
include the area of the base. If the question asked for thelateral surface area, then your answer wouldnotinclude
the bottom.

SA=πr^2 +

1

2

4 πr^2

=π( 62 )+ 2 π( 62 )

= 36 π+ 72 π= 108 πcm^2

Example 4:The surface area of a sphere is 100πin^2. What is the radius?

Solution:Plug in what you know to the formula and solve forr.

100 π= 4 πr^2

25 =r^2

5 =r

Example 5:Find the surface area of the following solid.

Solution:This solid is a cylinder with a hemisphere on top. Because it is one fluid solid, we would not include the
bottom of the hemisphere or the top of the cylinder because they are no longer on the surface of the solid. Below,
“LA” stands forlateral area.

SA=LAcylinder+LAhemis phere+Abase circle

=πrh+

1

2

4 πr^2 +πr^2

=π( 6 )( 13 )+ 2 π 62 +π 62

= 78 π+ 72 π+ 36 π

= 186 πin^2