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What is the Formula for the Volume of a Cone?

What is the formula for the volume of a cone?

Summary

  1. The bases of both the cylinder and the cone are circles
  2. The height of each solid is 6 meters
  3. The radius of each base is 3 meters
  4. V stands for volume
  5. B is the area of the base
  6. h is the height of the solid
  7. The volume of a cone is 1/3 of the volume of a cylinder
  8. The area of a circle is always πr2
  9. π, or pi, is an irrational number that we can approximate to 3.14

Notes

    1. The radius of the cylinder's base is 3 meters
    2. The radius of the cone's base is also 3 meters
    1. 'm' stands for meters
    1. Our cone and our cylinder have the same base and height
    2. So the volume of the cone is 1/3 the volume of the cylinder
    1. We can find the formula for the volume of a cone using the formula for the volume of a cylinder
    2. The volume of a cylinder is V=Bh
    3. V stands for volume
    4. B is the area of the base
    5. h is the height of the cylinder
    1. Remember, the volume of a cylinder is V=Bh
    2. V stands for volume
    3. So we can take 1/3 of the volume of a cylinder to get the volume of a cone
    1. The area of the base of a cone is always the area of a circle, or πr2
    2. B stands for the area of the base, in this case a circle
    3. π, or pi, is an irrational number that we can approximate to 3.14
    4. r is the radius of the circle
    5. V stands for volume
    6. h is the height of the cone
    1. V stands for volume
    2. π, or pi, is an irrational number that we can approximate to 3.14
    3. r is the radius of the base, which is 3, so we can plug 3 in for r
    4. h is the height of the cone, which is 6, so we can plug 6 in for h
    5. Since we found a volume, our units are in meters cubed, or m3
    1. V stands for volume
    2. π, or pi, is an irrational number that we can approximate to 3.14
    3. r is the radius of the base, which is 3, so we can plug 3 in for r
    4. h is the height of the cone, which is 6, so we can plug 6 in for h
    5. Since we found a volume, our units are in meters cubed, or m3
    1. If we did the problem correctly, then the volume of the cone should be 1/3 the volume of the cylinder
    2. The volume of the cylinder was 169.56
    3. Dividing by 3 is the same as multiplying by 1/3
    4. 56.52 was what we got for the volume of the cone
    5. So that means our formula is correct!