The formula calculates the area around the dead cone, the total area of ​​the dead-end cone, the volume of the dead-end cone

In the article below, TipsMake.com will introduce and share details to readers some of the topics related to the formula of calculating the volume of dead-end cones, the area around and the whole of the dead-end cone. Please read along for reference.

As learned from the previous article, the pyramid is formed when rotating a right triangle around its axis (a right-angled edge) one round.

When the cone is cut by a plane parallel to the bottom, the plane in the cone is a circle. The image between the aforementioned plane and the bottom face is called a dead end.

Understandably, a dead-end cone is a shape with two bottoms, two circles with different large and small radii lying on two parallel planes with a center line of symmetry axis.

Calculate the area of ​​the penguin cone

The area of ​​a penguin cone is often referred to with two concepts: ambient and full.

The area around the dead-end cone only covers the area of ​​the surrounding surface, surrounding the dead-end cone, not including the area of ​​the two bottoms.

The total area is calculated as the magnitude of the total occupied space, including the surrounding area and the area of ​​the two round bottoms.

As follows:

The formula calculates the area around the dead cone, the total area of ​​the dead-end cone, the volume of the dead-end cone Picture 3

There are truncated cones with 2-sided radii of r 1 and r 2 , the height of the cone is h , the line of birth is l , there will be the following related formulas:

Formula to calculate the surrounding area: equal to the surrounding area effect of large cones and small cones

The formula calculates the area around the dead cone, the total area of ​​the dead-end cone, the volume of the dead-end cone Picture 4

Inside:

1. S _around is the area around the penguin cone.
2. r 1 and r 2 are the 2 bottom radii of the truncated cone.
3. l is the length of the path of the dead end.

The formula for calculating the total area: equal to the surrounding area plus the area of ​​2 bottoms.

The formula calculates the area around the dead cone, the total area of ​​the dead-end cone, the volume of the dead-end cone Picture 5

The formula calculates the area around the dead cone, the total area of ​​the dead-end cone, the volume of the dead-end cone Picture 6

Calculate the volume of the penguin cone

The dead-end cone is the amount of space that the dead-end cone occupies.

Formula to calculate the volume of a dead cone: by the volume of a large cone and a small cone.

The formula calculates the area around the dead cone, the total area of ​​the dead-end cone, the volume of the dead-end cone Picture 7

Inside:

1. V is the volume of the penguin cone.
2. r 1 and r 2 are the 2 bottom radii of the truncated cone.
3. h is the height, the distance between the two bottoms of the dead end.

You can easily see that we often catch a dead-end cone in life like a bucket or a lampshade . Hopefully, through the above article, you have a better understanding of penguin cones and how to calculate the area. , how the volume of a dead cone.