Surface Area of Circular SolidsLesson 12.3

cylinder

cone

sphere

Cylinder: Contains 2 congruent parallel bases that are circles.Right circular cylinder perpendicular line from center to each base.

Net:h

r

Theorem 113: The lateral area of a cylinder is equal to the product of the height and the circumference of the base.

LAcyl = Ch = 2πrh(C = circumference, h= height)

h

r

The total area of a cylinder is the sum of the cylinder’s lateral area and the areas of the two bases.T.A. = 2πr2 + 2πrh

Find the surface area (total) of the following cylinder:

10cm

7cmTA = 2πr2 + 2πrhTA = 2π(72) + 2π(7)(10)TA = 98π + 140πTA = 238π cm2

Cone: base is a circleSlant height and lateral height are the same.

l

Cone will mean a right cone where the altitude passes through the center of the circular base.

Net:

Theorem 114: The lateral area of a cone is equal to1/2 the product of the slant height and the circumference of the base.

LA = ½Cl = πrlC = Circumference & l = slant height

Find the surface area of the cone.The diameter is 6 & the slant height is 8.

TA = πr2 + πrl = π(3)2 + π3(8) = 9π + 24π = 33π units2

The total surface area of a cone is the sum of the lateral area and the area of the base. TA = πr2 + πrl

Sphere: has NO lateral edges & No lateral areaPostulate: TA = 4πr2 r = radius of the sphere

Find the total area of the sphere:

TA = 4πr2

= 4π52

= 100π units2

As a team, find the surface area of the following shape. Only find the area of the parts you can see.

16cm

10cm

17cm

1. Lateral area of a cone,2. Plus the lateral area of the cylinder,

3. Plus the surface of the hemisphere.

πrl = π8(17) = 136π

2πrh = 2π(8)(10) = 160π

4πr2 = (1/2)4π(82) = 128π

4. Add them up: 136π + 160π + 128π = 424π units2