SURFACE AREA OF SOLIDS

March 22, 2010

Three-Dimensional Figures

Prism – a 3D solid with two parallel, congruent faces called bases

Pyramid – a 3D solid with one base that is any polygon; the other faces are triangles

Cylinder – a 3D solid that has two parallel, congruent circular bases connected with a curved side

Surface Area

Surface area refers to the sum of the areas of all the surfaces of a 3D figure.

Also called Total Surface Area (TSA) Examples:

wrapping paper orange

Lateral Surface Area

Lateral surface area of a solid only includes the faces or surfaces that make up the sides of the solid (not the base(s))

Examples: Soup can label

With a partner, you will determine the surface area of various geometric solids.

How Do You Find the Surface Area of a Solid?

4*s2 where s = length of side

6*s2

4*s*h, where s=length of side of base, h = height(2*s2)+(4*s*h)

3*s*h, where s=length of side of base, h = height of prism

3/2*s*l, where s=length of side of base, l=slant height

(3*s*h)+(s*a) where a=altitude of triangle

(1/2*s*a)+(3/2*s*l) where a =altitude of triangle at base2*s*l, where s=length of side of base, l=slant heights2 + (2*s*l)

2*π*r*h, where r = radius, h = height(2*π*r2)+(2*π*r*h)

Practice

Both containers hold about the same amount of pineapple juice. Does the box or the can have a greater surface area?

6 cm

9 cm9 cm

5 cm

5 cm

Practice

6 cm

9 cm

Surface Area of can

rhrS 22 2 )9)(3(2)3(2 2 S

5418 S272 cmS 22.226 cmS

Practice

Surface Area of box

)4()2( 2 shsS ))9)(5(4()5*2( 2 S

18050S2230 cmS

9 cm

5 cm

5 cm

Practice

Since 230cm2 > 288.2cm2, the box has a greater surface area.

Practice – Architecture

The Louvre museum in Paris has a huge square glass pyramid at the entrance with a slant height of about 92 feet. Its square base is 116 feet on each side. How much glass did it take to cover the pyramid?

Practice

92 feet

116 feet

Find the lateral area only since the bottom of the pyramid is not covered in glass.

slLSA 2)92)(116(2LSA2344,21 ftLSA