The formula for calculating the area around the cone, the full area of ​​the cone, cone volume, v cone

In the following article, Quantrimang.com will introduce and share details to readers some content related to the topic of the formula for calculating the cone volume, the surrounding area and the whole cone. Invite you to refer.

Pyramid Created when rotating a right triangle around its axis (a right angle).

Calculate the cone area

The cone area is often mentioned with two concepts: surrounding and full.

• Surrounding area The cone only includes the surrounding surface area, surrounding the cone, not the bottom area.
• Full area Calculated as the magnitude of the entire occupied space, including the surrounding area and the round bottom area.

Specifically as follows:

There is a square triangle at O, turning around the right corner of the fixed OA, a cone.

The edge of the scanner creates the bottom of the cone is a circle of center O. The edge of AB sweeps the surrounding face of the cone, each of its position is called a birth line, for example AB is a birth line. A is the peak and the pond is the height of the cone.

The formula for calculating the surrounding area: is half the product of the circumference of the bottom circle and the length of the birth line.

Applicable to the specific example above is: In there: Saround is the area around the cone. r is a cone -bottom radius. l Is the length of the cone line.

Formula for calculating total area: equal to the surrounding area plus the area of ​​the bottom.

Calculate the volume of cone

Cone volume Is the amount of space that the cone occupies.

Formula for calculating cone volume: equal ¹/₃ The area of ​​the bottom surface with height

In there:

• V is the cone volume.
• r is the bottom radius of the cone.
• h is the height, the distance between the peak and the bottom of the cone.

Determining the birth line, the height and the bottom radius

High roads are the distance from the center of the bottom to the top of the pyramid.

The birth line is a distance from any point on the bottom circle to the top of the pyramid.

Because the cone is formed when rotating a right triangle around the axis of a square corner of it, it is possible to see the height and the bottom radius is the two square angles of the triangle, and the birth line is the mysterious edge.

Therefore, when we know that the road is high and the bottom radius, we can calculate the path of birth by the formula:

Know the height and the birth line, calculate the bottom radius according to the formula:

Above are the formulas to calculate the surrounding area, total area and volume of the cone. Thank you for watching the article.