How to Calculate the Volume of a Truncated Cone: Step-by-Step Guide
A truncated cone is a cone with its top cut off parallel to the base. Its volume is the full cone minus the small cone removed, which simplifies to a formula using both radii and the height between them.
- (( R ) =) radius of the larger base
- (( r ) =) radius of the smaller base (the section that was removed)
- (( h ) =) height of the frustum (not the original cone’s height)
Worked examples: volume of a truncated cone
Practice questions on truncated cone volume
- What is the volume of a frustum with ( R = 10 text{ cm}), ( r = 6 text{ cm}), and ( h = 12 text{ cm})?
- A truncated cone has ( R = 15 text{ cm}), ( r = 5 text{ cm}), and ( h = 20 text{ cm}). What is its volume?
- ( approx 2461.76 text{ cm}^3 )
- ( approx 6803.3 text{ cm}^3 )
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