If the volume of a cone is equal to one-third the volume of a cylinder with the same base and height, explain why this relationship holds true.
Real Tutor Solution
Answer
Solution
Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.
Reviewed and approved by the UpStudy tutoring team
Mind Expander
The relationship holds true because of the geometric principles governing the shapes. The formula for the volume of a cylinder is V = πr²h, while for a cone, it’s V = (1/3)πr²h. The factor of one-third emerges from the way a cone tapers to a point, meaning it occupies less space than a cylinder. If you imagine filling a cone with water, the cone can only hold a third of what the cylinder can with the same base and height since it’s not as wide at the top! Moreover, this volume relationship can be tested by visualizing pouring the cone's contents into the cylinder. If you had three identical cones, their combined volume would perfectly fill the cylinder to the brim! This captivating connection between these basic shapes showcases the beauty of geometry in action, where even simple mathematical principles have far-reaching implications.