Bell Work: Use substitution to solve for x and y: x – 2y = -1 2x – 3y = 4

Answer: (11, 6)

Lesson 60: Geometric Solids, Prisms and Cylinders

In lesson 15 we defined a geometric solid as a geometric figure that has three dimensions. Here are some examples of geometric solids.

Prism: a geometric solids where two faces (bases) are identical and parallel polygons and where the other faces are parallelograms (lateral faces)

Altitude*: in a prism it is a perpendicular segment joining the planes of the bases. The length of the altitude is the height of the prism.

Right Prism*: a prism whose lateral edges are at right angles to the bases. Note that in a right prism, the lateral edges are also altitudes.

Prisms are classified and named according to the shape of their bases.

A cylinder is like a prism except that its base are closed curves instead of polygons. The curved surface between the base is called the lateral surface. The segment joining the centers of the bases is called the axis of the cylinder. The altitude of a cylinder is a perpendicular segment joining the planes of the bases.

Note that in a right cylinder, the axis is also its altitude.

The volume of a prism can be easily computed given the area of a base and the height. Since a cylinder is like a prism, the volume of a cylinder is computed in the exact same way as the volume of a prism.

Volume of prisms and cylinders:  The volume of a prism or a cylinder is equal to the area of a base times the height.

Example: The area of a base of a right pentagonal prism is 28 square cm and the length of a lateral edge is 10 cm. find the volume of the right pentagonal prism.

Answer: Volume = (area of base)(height) = (28 cm )(10 cm) = 280 cm 2 3

We define the lateral surface area of a prism or a cylinder to be the area of all external surfaces except the bases. Unfortunately, there is no simple way of computing lateral surface areas of prisms or cylinders unless they are right prisms or right cylinders.

Lateral Surface Area of Right Prisms and Right Cylinders:  The lateral surface area of a right prism or a right cylinder is equal to the perimeter of a base times the height.

To find the surface area of a prism or a cylinder, we add the areas of the bases to the lateral surface area.

Example: Find the lateral surface area of this right prism whose bases are regular pentagons. Dimensions are in meters. 15 8

Answer: Lateral Surface Area = (perimeter of base)(height) = (40m)(15m) = 600 meters 2

HW: Lesson 60 #1-30