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Are The Volume Of Cone And A Cylinder Related? | BYJU'S Fun Facts
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Are The Volume Of Cone And A Cylinder Related? | BYJU'S Fun Facts

Introduction

The video introduces the concept of volume and explores the relationship between the volumes of a cone and a cylinder.

Volume of a Cylinder

  • A cylinder is a three-dimensional solid that connects two parallel circular bases joined by a curved surface.
  • The volume of a cylinder is equal to the area of its base multiplied by its height.
  • The formula for calculating the volume of a cylinder is given as V = πr²h, where r is the radius of the circular base and h is its height.

Volume of a Cone

  • A cone is a three-dimensional object with a circular base and pointed top joined by a curved surface.
  • If we have two objects with identical heights and bases, then their volumes are related in such that one-third times the volume of one object equals to another.
  • For example, if we have two objects with identical heights and bases, then their volumes are related in such that one-third times the volume of one object equals to another. Therefore, if we have two objects with identical heights but different shapes (e.g., cone and cylinder), then their volumes will be related in this way.

Relationship Between Pyramids and Prisms

This section explores how pyramids relate to prisms in terms of their volumes.

Triangular Pyramid vs Triangular Prism

  • If we have two objects with identical heights and bases (triangular pyramid vs triangular prism), then their volumes are related in such that one-third times the volume of one object equals to another.
  • Therefore, all pyramids have one-third the volume of prisms provided they have same bases and heights.

Changing Bases

  • We can keep changing our bases from pentagonal, hexagonal, and so on, and the relationship will still remain the same.
  • A cone is actually a circular pyramid and a cylinder is a circular prism.
  • Therefore, all pyramids have one-third the volume of prisms provided they have same bases and heights.
Video description

Both cones and cylinders are three dimensional in shape and have circular bases and curved surfaces. When we flip them, we find that one has a pointed top and the other an identical circular top. Their heights are also the same. In that case, are the volumes of a cone and a cylinder related? In this video, we answer this fascinating question for you! So sit back and enjoy! For more such interesting Fun Facts, like, share and subscribe to BYJU’S. 👉 Subscribe to BYJU'S - http://bit.ly/2IYECcw 👉 Install the BYJU'S App - http://bit.ly/Playstore-Appstore 👉 For more interesting content - https://blog.byjus.com/the-learning-tree/ Video Chapters 0:00 - 0:33 Introduction 0:34 - 2:48 Volume of a cylinder 2:49 - 4:27 Relationship between the volume of cone and cylinder 4:28 - 6:19 How does cone and cylinder with different base looks? #VolumeOfCone #VolumeOfCylinder #AreaOfCircle #volumeofconeformula #Volumeofcylinderformula #Areaofcircleformula #BYJUSFunFacts #FridayFunFacts #BYJUSTheLearningApp