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.


Week 5 – Converting Units of Measurement

This week in math we learned how to convert units of measurement in a simple way between both longer/shorter units within the same system, and between the metric and imperial systems.

Easy to do, you simply need to know how many of one unit is equal to the other unit.

Example: The units that you wish to convert go on the left (6780cm), the units that you wish to convert to go in the numerator position (1m) and however many units of one equal the other (100cm) in the denominator.

Then simply evaluate your expression

The same can be done for converting units between the metric and imperial systems.

Example: If you know 1ft is equal to 0.3048m, then you repeat the same steps again.

And evaluate.