Mathematics II Geometric Measurement and Dimension


Geometric Measurement and Dimension


Explain volume formulas and use them to solve problems.
1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid,
and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. tools-icon
5. Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k2, and k3,
respectively; determine length, area and volume measures using scale factors.
6. Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer,
and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve
real-world and mathematical problems.