4 2 Explain Volume Formulas and Solve Real

4. 2 Explain Volume Formulas and Solve Real World Problems Instructional Days: 10

Common Core Content Standards Congruence � Experiment with transformations in the plane G-CO Geometric Measurement and Dimension � Explain volume formulas and use them to solve problems G-GMD � G-CO. 1 Know precise definitions of circle, and distance around a circular arc. � G-GMD. 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. � G-GMD. 3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★ Modeling with Geometry � Apply geometric concepts in modeling situations G-MG � G-MG. 2 Apply concepts of density based on area and volume in modeling situations (e. g. , persons per square mile, BTUs per cubic foot). ★ � G-MG. 3 Apply geometric methods to solve design problems (e. g. , designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★ Circles G – C � Find arc lengths and areas of sectors of circles [Radian introduced only as unit of measure] � G-C. 5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Standards of Math Practice SMP 3 Construct viable arguments and critique the reasoning of others �Give informal arguments for circumference, area, and volume formulas. SMP 4 Model with mathematics �Apply circumference, area, and volume formulas to real world situations. SMP 5 Use appropriate tools strategically �Use models of three-dimensions objects SMP 6 Attend to precision �Use correct units of measure when finding circumference, area, and volume

Essential Questions How can you determine the volume for a compound threedimensional object? When would you use volume in the real world? Why do we need pi when finding area and volume? How are arc length and area of a sector related to circle formulas? When is it appropriate to use radian measure?