Geo.5 Solid Geometry
- I can draw the two-dimensional shape that creates a particular three-dimensional solid when rotated using a given axis.
- I can identify the three-dimensional solid created by rotating a two-dimensional figure using a linear axis.
- I can identify the three-dimensional shape that generates a set of cross sections.
- I can visualize and draw multiple cross sections of a three-dimensional figure.
- I know that a pyramid’s cross sections are dilations of its base with scale factors ranging from 0 to 1.
- I know that when figures are dilated by a scale factor of $k$, their areas are multiplied by $k^2$.
- I can use square root graphs and do calculations to interpret the relationships between scale factors and areas.
- I know that when a solid is dilated by a scale factor of $k$, its surface area is multiplied by $k^2$ and its volume is multiplied by $k^3$.
- I can create and describe graphs that show relationships between volumes and scale factors.
- I can work backwards from a volume or surface area scaling to find a scale factor.
- I can calculate scale factors for lengths, surface areas, and volumes if I’m given any 1 of the 3 factors.
- I can calculate volumes of solids that are composed of cylinders.
- I can explain how finding the volume of a prism relates to finding the volume of a cylinder.
- I know that if two solids have equal-area cross sections at all heights, they have the same volumes.
- I can calculate volumes of right and oblique prisms and cylinders and figures composed of prisms and cylinders.
- I can explain the relationships between pyramids, cones, prisms, and cylinders.
- I can explain why the volume formula for pyramids and cones is $V=\frac13Bh$.
- I can calculate volumes of pyramids and cones.
- I can work backward from a given volume to find possible dimensions of a pyramid or cone.
- I can use the Pythagorean Theorem and trigonometry to help calculate volumes of prisms, cylinders, cones, and pyramids, including solids of rotation.
- I can use surface area and volume relationships to solve problems.
- I can solve problems involving density and volume.
- I know that the density of an object is the ratio between its mass and its volume.
- I can use cube root and square root graphs to solve geometric problems.