Chapter 10: Surface Area and VolumeObjectives: Students will be able to find the surface area and volume of three dimensional figures.

Prism:• 2 congruent, parallel faces (called the bases). • The other faces of the prism are called lateral faces• Named by the shape of its base• Altitude: perpendicular segment joining the bases• Height: the length of the altitude

Lateral Surface Area:• The sum of the areas of the lateral faces• Area of the sides (not including the bases)

For a Right Prism: LA = php=perimeter of baseh= height

Surface Area:• Sum of lateral surface area and the area of the 2 bases• Find lateral surface area and then add the area of the bases

For a Right Prism: SA= LA + 2BB= area of the baseSo…SA = ph + 2B

Examples: Find LA and SA for each figure. Round to nearest tenth, if necessary.

1. 2.

Find the LA and SA of the trapezoidal prism.

Area of a trapezoid:

212

1bbhA

Cylinder (bases are circles)

LA = 2rh

Surface Area of Cylinders:

SA= 2rh + 2r2

Find the LA and SA of the cylinder.

1. (Round to nearest hundredth) 2. (Leave answer in terms of pi)

Pyramids and Cones

Pyramid:The base is any polygon and the other faces (lateral faces) are triangles that meet at a common vertex

Cone: Pyramid whose base is a circle.

Slant Height (l):

The length of the altitude of the lateral face of the pyramid

Lateral Surface Area of Pyramids and Cones:

Lateral Surface Area of Pyramid:

LA = ½ plp= perimeter of basel= slant height

Lateral Surface Area of Cone:

LA = rl

Any ideas how we came up with the formula for LA of a cone?

Total Surface Area of Pyramids and Cones:

Pyramid: SA = LA + BB= area of the base

Cone: SA = LA + r2

Find the slant height. Round to the nearest tenth, if necessary.

Find the LA and SA of the pyramid.

1. 2.

Find LA and SA of the cone.

1. (Round to nearest tenth) 2. (Leave in terms of pi)

Surface Area of a Sphere:

24 rSA

Find the surface area of the sphere.

1. (Leave in terms of pi). 2. (Round to nearest tenth)

Cross Section• The shape you get when you “slice” a 3 dimensional figure

VOLUME• The space that a figure occupies

• Measured in cubic units

• When finding volume of pyramids and cones, need to use the height, not slant height. The height is perpendicular to the base.

VOLUME FORMULAS:Right Rectangular Prism: Any Pyramid:V= lwh Any Right Prism: B = area of the base V= BhB= area of the base Cone:

Cylinder:

Square Pyramid: Sphere:

hsV 2

3

1

BhV3

1

hrV 2

3

1

3

3

4rV

hrV 2

Find the volumes. Round the nearest tenth, if necessary.

1. 2.

Find the volumes. Round the nearest tenth, if necessary.

3. 4.

Find the volumes. Round the nearest tenth, if necessary.

5. 6.

Find the volumes. Round the nearest tenth, if necessary.

7. 8.