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Overview
Mathematics at Work 11
Measurement
1. Solve problems involving SI and imperial units in surface area measurements and verify solutions
1.5 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
NS Curriculum Aligned