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

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Chapter 10: Surface Area and Volume Objectives: 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 = ph p=perimeter of base h= 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 + 2B B= area of the base So… 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:

Cylinder (bases are circles)

Surface Area of Cylinders:

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:

Total Surface Area of Pyramids and Cones:

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:

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= Bh B= area of the baseCone: Cylinder: Square Pyramid:Sphere:

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.

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