The purpose of this lesson is to expand student knowledge of using the surface area formulas. Students will use surface area formulas to calculate the surface area of cylinders, cones, and spheres, as well as calculate missing dimensions.
Students will use many previously learned skills in this lesson in order to calculate surface area and the missing dimensions when given the surface area. Students will need to have an understanding of substitution and solving equations for a variable. Students will also need to be familiar with converting units of measure.
At the end of this lesson, students will be able to:
use formulas to solve for problems involving surface area of cylinders.
use formulas to solve for problems involving surface area of cones.
use formulas to solve for problems involving surface area of spheres.
use formulas to solve for missing dimensions involving surface area of cylinders, cones, and spheres.
apply concepts of density in the context of area.
Student Target
“I can use formulas to calculate
the surface area of a cylinder.” the surface area of a cone.” the surface area of a sphere.” for the missing dimension when given the surface area.” “I can apply concepts of density for a given area.”
CCR Focus Standards
Geometry - Level C
Geometry - Level D
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Supporting Standards
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2.
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* [Also see 7.RP.3]
Standards for Mathematical Practice
Make sense of problems and persevere in solving them. (MP.1)
Reason abstractly and quantitatively. (MP.2)
Attend to precision. (MP.6)
KYAE Employability Standards
E.1 Effectively contribute to a team through cooperation, leadership, and giving and accepting critical feedback to work toward a common goal.
E.5 Utilize resources responsibly.
E.6 Identify and effectively use skills and materials needed for a particular task.