Public learning track
Surface Area and Volume of 3D Solids
7th Grade · Math · Open Global Math
8 lessons
Goal
Calculate lateral surface area, total surface area, and volume of prisms, pyramids, cylinders, and composite solids, modeling volume relationships.
Featured Diagrams
Lateral and Total Surface Area of Prisms and Cylinders
8 lessons
0 of 8 done
- 1Lateral and Total Surface Area of Prisms and CylindersUp nextStart
- 2Lateral and Total Surface Area of Pyramids and ConesPremiumNot started yet
- 3Calculating Volume of Right Prisms Using Uniform Cross SectionNot started yet
- 4Calculating Volume of CylindersNot started yet
- 5Modeling the One-Third Relationship Between Pyramids and PrismsNot started yet
- 6Calculating Volume of Right Pyramids and ConesNot started yet
- 7Calculating Volume of Composite Structures: Prisms and PyramidsNot started yet
- 8Solving Real-World Engineering and Packaging Measurement ProblemsNot started yet
Curriculum Framework
7th Grade · Math · Open Global Math
1
9 lessons
Angle Relationships and Parallel Lines
Identify and calculate unknown angles using complementary, supplementary, vertical, and parallel line transversal relationships with algebraic equations.
2
7 lessons
Triangle Theorems, Angles, and Inequalities
Apply interior and exterior angle theorems, side-angle relationships, and the triangle inequality to classify and solve triangles.
3
7 lessons
Triangle Congruence Criteria and Proofs
Prove triangles congruent using SSS, SAS, ASA, AAS, and HL criteria and deduce corresponding parts.
4
9 lessons
The Pythagorean Theorem and Right Triangle Geometry
Prove, calculate, and apply the Pythagorean theorem and its converse to 2D and 3D real-world problems.
5
7 lessons
Quadrilaterals, Polygons, and Angle Sums
Classify quadrilaterals, prove polygon properties, and calculate interior and exterior angle sums of n-sided polygons.
6
8 lessons
Deductive Reasoning, Logic, and Geometric Proofs
Construct direct proofs, converse statements, counterexamples, and proofs by contradiction to establish geometric truths.
7
9 lessons
Circle Foundations, Pi, Circumference, and Arcs
Define pi, calculate circumference and arc length, and analyze chords, tangents, and central and inscribed angles.
8
7 lessons
Area of Circles, Sectors, and Composite 2D Shapes
Derive circle area, calculate sector and segment areas, and solve perimeter and area for composite plane figures.
9
9 lessons
Geometric Constructions and Loci
Execute precise geometric constructions using compass, straightedge, protractor, and dynamic geometry software.
10
7 lessons
Rigid Transformations and Symmetry in the Plane
Perform and describe translations, reflections, and rotations on and off the coordinate plane and identify symmetries.
11
9 lessons
Dilations, Similarity, and Scale Drawings
Apply dilations, establish triangle similarity criteria (AA, SAS, SSS), and solve scale drawing and perimeter/area ratio problems.
12
6 lessons
Introduction to Right Triangle Trigonometry
Define sine, cosine, and tangent ratios, compute exact values for 30°, 45°, 60°, and solve right triangles.
13
7 lessons
3D Visualization: Orthographic Views, Nets, and Cross-Sections
Represent 3D objects with front/top/side orthographic projections, nets, isometric drawings, and plane cross-sections.
14
8 lessons
Surface Area and Volume of 3D Solids
Calculate lateral surface area, total surface area, and volume of prisms, pyramids, cylinders, and composite solids, modeling volume relationships.