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Overview
Mathematics at Work 11
Geometry
5. Model and draw 3-D objects and their views
5.1 Surface area of 3-dimensional shapes
Surface Area of 3D Shapes
The total area of all the faces and surfaces of a solid, with formulas for prisms, cylinders, cones, and spheres.
What You'll Learn
Surface area is the total area of all faces and surfaces of a solid, in square units.
Rectangular prism: 2 times (lw plus wh plus lh).
Cylinder: 2 pi r squared plus 2 pi r h; sphere: 4 pi r squared.
Unfolding a solid into a net turns surface area into a sum of flat areas.
Surface area measures the outside; volume measures the space inside.
What You'll Practice
1
Finding dimensions of single blocks from composite rectangular objects
2
Calculating total surface area by adding areas of all six rectangular faces
3
Computing surface area ratios between parts and whole objects
4
Working with multi-step problems involving division and surface area formulas
Why This Matters
Understanding surface area is essential for real-world applications like calculating paint needed for walls, wrapping packages, or designing containers. This skill is foundational for geometry, engineering, and architecture courses, and helps you visualize and measure 3D space accurately.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Learning resources
Skills
Surface Area
Rectangular Prisms
3D Geometry
Ratios
Spatial Reasoning
Measurement
Problem Solving
NS Curriculum Aligned