Examples for

Common Core Math: High School Geometry: Measurement & Dimension

Students reason with and apply formulas for volumes of geometric solids, including solving for unknown measurements and exploring relationships between shapes such as cylinders, cones and pyramids. Students draw connections between two- and three-dimensional figures by taking two-dimensional cross sections of three-dimensional solids and by rotating two-dimensional figures to form three-dimensional solids.

Common Core Standards

Get information about Common Core Standards.

Look up a specific standard:

CCSS.Math.Content.HSG-GMD.B.4
geometric measurement & dimension cc standard a.3

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high school measurement and dimension common core standards

Cross Sections

Relate two-dimensional and three-dimensional objects.

Visualize cross sections of solids (CCSS.Math.Content.HSG-MD.B.4):

cross section of a cylinder
sphere cross section
cross sections of a cone's surface

Rotate a two-dimensional shape to create a three-dimensional solid (CCSS.Math.Content.HSG-MD.B.4):

revolve y = sqrt(1 - x^2) around the x-axis
rotate the region between 0 and -2x + 2 with 0 < x < 1 around the y-axis
rotate sin x with 0<x<pi around the x-axis

Volume

Use volume formulas for geometric solids.

Get the formulas for common geometric measurements (CCSS.Math.Content.HSG-MD.A.1):

circumference of circle
area of circle
volume formula for cylinder
volume of a pyramid with base area B and height h
cone volume
volume of a sphere with radius r
Cavalieri's principle

Solve problems involving volumes of solids (CCSS.Math.Content.HSG-MD.A.3):

What is the radius of a cone with volume v and height 7
volume of cylinder with height 4 feet and circumference 34 inches
if the volume of a sphere is 8 cm^3, what is its radius?
sphere, surface area=1
height of cone with radius 8 in and volume 2542 in^3
volume of cone with r = 2 vs volume of cylinder with r = 2

RELATED EXAMPLES

  • Common Core Math: Circles
  • Common Core Math: Congruence
  • Common Core Math: Expressing Geometric Properties with Equations
  • Common Core Math: Modeling with Geometry
  • Common Core Math: Similarity & Trigonometry
  • Geometry