Bell Work: Graph the inequality:

-3 < x < 3

Answer:See Example

Lesson 95:Slant Heights of Pyramids and Cones

The term height in geometry generally means the perpendicular distance from the highest point of a figure to its base. The heights of the pyramid and cone are equal. Both are the distance from the apex of the solid to the point on the base directly below the apex. We use the height to calculate the volume.

For pyramids and cones we are also interested in another measure called the slant height, which is the diagonal distance along the surface from the apex to the base.

We use the slant height to calculate surface area. We will learn more about the surface areas of pyramids and cones in lesson 100.

If we look at a vertical cross section of a pyramid or cone at the apex, we see that the cross section is an isosceles triangle. The height divides the cross section into two right triangles. The slant height is the hypotenuse of one of the right triangles.

If we know the dimensions of the base and the height of the solid, then we know the measures of two legs of the right triangles. We can use the Pythagorean Theorem to find the hypotenuse.

Example:Calculate the slant height of the cone.

12 cm

10 cm

Answer:13 cm

Example:Arman is building a model of the Great Pyramid to approximate proportions. The base of the pyramid will be a square 30 cm on each side. He wants the height of the pyramid to be 20 cm. what should be the slant height of the triangular faces? Sketch a net of the Great Pyramid model Arman is building.

Answer:25 cm.

HW: Lesson 95 #1-25