Week 6 – Slant Height, Pyramids, and Cones

This week in math 10 we learned about right pyramids, cones, and how to calculate slant height.

To calculate the slant height of right pyramids, you need to have the height and half of the length. Then you can use the Pythagorean theorem to find the hypotenuse (your slant height). Then you can use your slant height when you calculate the total surface area or volume.

Example: When you have the height (3 in this case) and the side length (8), you can calculate the slant height. Take half the side length (4) and use it and the height in the Pythagorean theorem. In this case 3^2 + 4^2 = 25 = c^2. Therefore 5 = c, and 5 is your slant height. You can then plug the slant height into the surface area and volume equations.

The Pythagorean Theorem principle is also used when calculating the slant height of a cone. The only difference is instead of using half the side length and the height to find the hypotenuse (slant height), you use the radius of the base and the height.


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