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Overview
Grade 10
Develop spatial sense and proportional reasoning
2. Solve problems using SI and imperial units for surface area and volume of 3-D objects including cones, cylinders, prisms, pyramids, and spheres
2.5 Surface area and volume of spheres
Surface Area and Volume of a Sphere
A sphere's surface area and volume both depend only on its radius, with no flat net.
What You'll Learn
A sphere is perfectly round: every surface point is the same distance (radius r) from the center.
Surface area = 4 times pi times r squared.
Volume = four-thirds times pi times r cubed.
A sphere has no flat net; its curved surface cannot be unrolled flat.
Both formulas use only the radius, unlike a cone which also needs height or slant height.
What You'll Practice
1
Finding surface area and volume of hemispheres with exposed circular bases
2
Calculating dimensions of capsule-shaped solids (cylinder with spherical ends)
3
Converting between circumference and radius to solve problems
4
Adding surface areas and volumes of combined geometric shapes
Why This Matters
Understanding spheres and composite solids is essential for real-world applications like calculating material needs for manufacturing, determining capacity of containers, and solving engineering problems. These skills build your spatial reasoning and prepare you for advanced geometry, physics, and calculus.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Learning resources
Skills
Spheres
Surface Area
Volume
Composite Solids
Hemispheres
Cylinders
Circumference
3D Geometry
MB Curriculum Aligned