Cone Frustum Volume

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Cone Frustum Volume Calculation:

  • r1 =

    Radius of the circular base

  • r2 =

    Radius of the top cirlce

  •  h =

    Height of the frustum at right-angles from the circular base to top circle

  •  V =

    Final volume of the conical frustum in cubic units

  •

    Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Cone Frustum Volume Formula

A conical frustum is a portion of a cone with a circular base and circular top. A frustum is made by cutting the tip off of a full cone. To calculate the conical frustum volume we need the radius of the base circle, radius of the top circle, and height between the two circles.

V = (πh/3)*(r12+r22+r1*r2)

Cone Frustum Volume Variables

Two radaii and a height value can be used to find the frustum volume.

Radius 1 (r1)
Radius of the circular base.
Radius 2 (r2)
Radius of the circular top.
Height (h)
Distance between the circular base and top circle at right-angles.
Volume (V)
Volume of the conical frustum in cubic units.

Cone Frustum Volume Solution

What is the volume of a conical frustum with a base radius of 4, top radius of 3, and height of 5?

  • V = (πh/3)*(r12+r22+r1*r2)
  • Formula used to calculate to volume
  • V = (3.14159 * 5/3)*(42+32+4*3)
  • Substitute in the calculation values. Using a value of 3.14159 for Pi
  • V = (3.14159 * 5/3)*(16+9+4*3)
  • Calculate the powers
  • V = (5.2359833)*(16+9+12)
  • Multiplication and division inside brackets
  • V = 5.2359833 * 37
  • Finish addition inside brackets
  • V = 193.7313821
  • Final multiplication
  • ~193.7313821 Cubic Units

The frustum with a base radius of 4, top radius of 3, and height of 5 will have a volume of about 193.73 cubic units (rounded to two decimal places).

Find the volume of a standard cone

Cone Volume