Formula for calculating the lateral area of ​​a cone, total area of ​​a cone, volume of a cone, V of a cone

In the article below, Quantrimang.com will introduce and share with readers in detail some content related to the topic of formulas for calculating the volume of a cone, the lateral area and the total area of ​​a cone. Please refer to it.

Table of Contents

• Calculate the area of ​​the cone
• Calculate the volume of a cone
• Determine the generator, altitude and base radius

A pyramid is formed by rotating a right triangle around its axis (a right angled side) one revolution.

Calculate the area of ​​the cone

The area of ​​a cone is often referred to in two terms: surrounding and total.

• The lateral area of ​​a cone only includes the surface area surrounding the cone, not the base area.
• The total area is calculated as the magnitude of the entire space occupied by the figure, including the lateral area and the area of ​​the circular base.

Specifically as follows:

Given a right triangle ABO at O, rotating around the fixed right angle side OA will give a cone.

The edge OB sweeps to form the base of the cone which is a circle with center O. Edge AB sweeps up the surrounding surface of the cone, each of its positions is called a generator, for example AB is a generator. A is the vertex and AO is the height of the cone.

Formula for calculating lateral area: equal to half the product of the circumference of the base circle and the length of the generating line.

Applied to the specific example above: In there: The perimeter is the area around the cone. ris the radius of the base of the cone. lis the length of the generator line of the cone.

Formula for calculating total area: equals lateral area plus base area.

Calculate the volume of a cone

The volume of a cone is the amount of space the cone occupies.

Formula for calculating the volume of a cone: equal to 1/3 of the base area multiplied by the height

In there:

• Vis the volume of the cone.
• ris the base radius of the cone.
• his the height, the distance between the top and the base of the cone.

Determine the generator, altitude and base radius

The height is the distance from the center of the base to the apex of the pyramid.

The generator is the distance from any point on the base circle to the top of the pyramid.

Because a cone is formed when a right triangle is rotated around the axis of one of its right-angled sides once, the height and the base radius can be considered as the two right-angled sides of the triangle, and the generator is the hypotenuse.

Therefore, knowing the height and base radius, we can calculate the generating line using the formula:

Knowing the height and the generator, calculate the base radius according to the formula:

Above are the formulas for calculating the lateral area, total area and volume of a cone. Thank you for following the article.