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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
2.4 Surface area and volume of cones
Surface Area and Volume of a Cone
A cone's surface area combines its circular base and unrolled lateral surface; its volume is one-third that of a matching cylinder.
What You'll Learn
A cone has a radius (r), height (h), and slant height (l), related by r squared plus h squared equals l squared.
Surface area = pi r squared (base) plus pi r l (lateral surface).
Volume = one-third pi r squared h, one-third of a matching cylinder's volume.
Unrolling a cone gives a circle (the base) plus a sector (the lateral surface).
For r=3, h=4 (so l=5): surface area is 24 pi and volume is 12 pi.
What You'll Practice
1
Finding slant height using the Pythagorean theorem with radius and height
2
Calculating surface area and volume of cones with given dimensions
3
Converting between feet and inches before applying formulas
4
Working with composite solids like hemispheres combined with cones
Why This Matters
Mastering cone calculations builds on your knowledge of circles, pyramids, and cylinders while preparing you for real-world applications in engineering, architecture, and design. From ice cream cones to traffic cones to rocket nosecones, these formulas help you solve practical problems involving three-dimensional objects.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Learning resources
Skills
Surface Area
Volume
Cones
Pythagorean Theorem
Slant Height
Composite Solids
Unit Conversion
3D Geometry
MB Curriculum Aligned