Use the Pythagorean theorem to unroll a cone and find its surface area with this interactive video from the School Yourself Geometry series.

Content Standard(s):

Mathematics MA2015 (2016) Grade: 9-12 Geometry

35 ) Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [G-GMD1]

Alabama Alternate Achievement Standards

AAS Standard: M.G.AAS.HS.35- Make a prediction about the volume of a container, the area of a figure, or the perimeter of a figure. Ex: how many cubes will go in one figure vs. another. Limit to cylinder, circle.

Mathematics MA2015 (2016) Grade: 9-12 Precalculus

38 ) (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. [G-GMD2]

Mathematics MA2019 (2019) Grade: 7

19. Describe the two-dimensional figures created by slicing three-dimensional figures into plane sections.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.7.19 Match two similar geometric shapes that are proportional in size and orientation.

Mathematics MA2019 (2019) Grade: 8

30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.8.30 Use the formulas for perimeter, area, and volume to solve real-world and mathematical problems (where volume problems are limited to finding the volume of cylinders and rectangular prisms).

Mathematics MA2019 (2019) Grade: 9-12 Geometry with Data Analysis

16. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Alabama Alternate Achievement Standards

AAS Standard: M.G.AAS.10.16 Given a cross section of a three-dimensional object, identify the shapes of two-dimensional cross sections (limited to sphere, rectangular prism, or triangular prism).

Mathematics MA2019 (2019) Grade: 9-12 Geometry with Data Analysis

17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.

Alabama Alternate Achievement Standards

AAS Standard: M.G.AAS.10.17 Compare and contrast the volume of real-world geometric figures.

Mathematics MA2019 (2019) Grade: 9-12 Geometry with Data Analysis

23. Develop definitions of rotation, reflection, and translation in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Alabama Alternate Achievement Standards

AAS Standard: M.G.AAS.10.21 Identify and/or model characteristics of a geometric figure that has undergone a transformation (reflection, rotation, translation) by drawing, explaining, or using manipulatives.