Diện tích xung quanh hình nón: công thức, bài tập ví dụ

The altitude is the length from the center of the base to the top of the cone.

The birth line is equal to the distance from any point on the base circle to the top of the cone.

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birth line length

Radius of the base of the cone

As we know, a cone is formed when we rotate a right triangle around the axis of one of its right angles. Therefore, the base radius and altitude can be considered as the two right angles of the triangle, and the birth line will be the hypotenuse. So when we know 2 of these 3 data, we can easily calculate the remaining data. Specifically:

r^2 = l^2 – h^2

Exercises to calculate the perimeter of a cone

Exercise 1: A cone with radius 4cm and height 7cm, find the surrounding area of ​​the cone.

In this exercise, first, we need to calculate the length of the birth path. Line length Birth is calculated according to the formula:

l^2 = r^2 + h^2

→ l = 8.06cm

Using the formula for the area around the cone, we have:

Sxq = .rl

= .4.8.06

= 101.23 cm2

Exercise 2: Given that the total area of ​​the cone is 375 cm. If the birth line ofi.if it is four times the radius, then the diameteri.the base of the cone isi.how much? Use = 3

Solution instructions are as follows:

According to the problem: l = 4r and = 3

The total area of ​​the cone is 375 cm2, so we have: 3 × r × 4 r + 3 × r2 = 375

<=> 12r2 + 3r2 = 375

<=> 15r2 = 375

=> r = 5

So the radius of the base of the cone is 5 => The diameter of the cone is 5.2 = 10 cm.

Here is the formula to calculate area around the cone and some other related formulas. According to the experience of Tran Hung Dao High School, depending on what data the question is for, you will be flexible to find the correct answer.

[rule_{ruleNumber}]

#Area #area #around #circle #cone #formula #exercise #exercise #examples

[rule_3_plain]

#Area #area #around #circle #cone #formula #exercise #exercise #examples

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In geometry, the surrounding area is one of the frequently used concepts. Our following article today wants to show you how to calculate the area around a cone – a very common shape in spatial geometry.
What is a cone?

Article table of contents

What is a cone Formula for area around a cone Formula for a cone Formula for total area of ​​a cone base radius, altitude, cone’s birthlineFind the height of a coneCone’s birthlineBody radius of a coneExercise for calculating the circumference of a cone

Before knowing the formula for calculating the surrounding area, we need to understand what a cone is.
In spatial geometry, a cone is a shape with a flat surface and an upward curved surface. The pointed end of the cone is called the top, and the flat surface is called the base.
In daily life, you can easily come across conical-shaped objects such as conical hats, ice cream cones, birthday hats, etc. It has 3 main characteristics:
One vertex is a triangle
There is 1 round side as the bottom side
Doesn’t have any edges
Formula for area around a cone
The perimeter of a cone includes the surface area around the cone, excluding the base area.
The area around the cone is equal to the product of Pi times the base radius times the cone’s generation line
Sxq = .rl
Formula to calculate area around a coneIn which:
– Sxq is the surrounding area
– is a constant, equal to 3.14
– r is the base radius
– l is the length of the birth line
Or you can use the following formula: “The area around the cone is half the product of the circumference of the base circle with the length of the birth line.” Because half the circumference of the circle is π.r.
Example: Given a cone whose base is center O and vertex A. The length of the radius from the center of the cone’s base to a base edge is 7cm, and the length of the birth line is 9cm. What is the area around the cone?
Answer: Sxq = π.rl = 3,14.7.9= 197.82 (cm)²
Refer to more Maths materials of Tran Hung Dao High School
Formulas of cones
Formula for total area of ​​a cone
The total area of ​​the cone includes both the surrounding area and the area of ​​the rounded base. Formula:
Stp = Sxq + Bottom = .rl + .r^2
Formula for volume of cone
The volume of a cone is the total amount of space it occupies, which is the product of the area of ​​the base and the height. Specifically:
V cone = .π.r^2.h
In there:
– V is the volume
– is a constant, equal to 3.14
– r is the base radius
– h is the altitude from the top to the bottom
Area around truncated cone
A truncated cone is a shape where part of the cone is cut off. The circumferential area of ​​a truncated cone includes the surrounding surface area, excluding the two base areas.
Formula for calculating the perimeter of a truncated cone
Sxq = .(r1+r2).l
Area around truncated coneIn which:
– Sxq is the surrounding area
– is a constant, equal to 3.14
– r1, r2 is the radius of 2 bases
– l is the length of the birth line
Total area of ​​truncated cone
Stp = Sxq + S 2 bottom = π.(r1+r2).l + π.(r1)^2 + π.(r2)^2
Total areaVolume of truncated cone
V = ⅓.π.h.((r1)^2 + (r2)^2 + r1.r2))
How to find the base radius, altitude, and birth line of a cone
Find the altitude of the cone
The altitude is the length from the center of the base to the top of the cone.
Formula for the height of a cone
h^2 = l^2 – r^2
Birth line of the cone
The birth line is equal to the distance from any point on the base circle to the top of the cone.
The length of the birth path of the cone
l^2 = r^2 + h^2.
length of the birth line Radius of the base of the cone
As we know, a cone is formed when we rotate a right triangle around the axis of one of its right angles. Therefore, the base radius and altitude can be considered as the two right angles of the triangle, and the birth line will be the hypotenuse. So when we know 2 of these 3 data, we can easily calculate the remaining data. Specifically:
r^2 = l^2 – h^2
Exercises to calculate the perimeter of a cone
Exercise 1: A cone has radius 4cm and height 7cm, find the perimeter of the cone.
In this exercise, first, we need to calculate the length of the birth path. The length of the birth line is calculated by the formula:
l^2 = r^2 + h^2
→ l = 8.06cm
Using the formula for the area around the cone, we have:
Sxq = .rl
= .4.8.06
= 101.23 cm2
Exercise 2: Given that the total area of ​​the cone is 375 cm. If the birth line is four times the radius, what is the diameter i.base of the jasmine cone? Use = 3
Solution instructions are as follows:
According to the problem: l = 4r and = 3
The total area of ​​the cone is 375 cm2, so we have: 3 × r × 4 r + 3 × r2 = 375
<=> 12r2 + 3r2 = 375
<=> 15r2 = 375
=> r = 5
So the radius of the base of the cone is 5 => The diameter of the cone is 5.2 = 10 cm.
Above is the formula for calculating the area around a cone and some other related formulas. According to the experience of Tran Hung Dao High School, depending on what data the question is for, you will be flexible to find the correct answer.

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#Area #area #around #circle #cone #formula #exercise #exercise #examples

[rule_2_plain]

#Area #area #around #circle #cone #formula #exercise #exercise #examples

[rule_2_plain]

#Area #area #around #circle #cone #formula #exercise #exercise #examples

[rule_3_plain]

#Area #area #around #circle #cone #formula #exercise #exercise #examples

5/5 – (1 rating)

In geometry, the surrounding area is one of the frequently used concepts. Our following article today wants to show you how to calculate the area around a cone – a very common shape in spatial geometry.
What is a cone?

Article table of contents

What is a cone Formula for area around a cone Formula for a cone Formula for total area of ​​a cone base radius, altitude, cone’s birthlineFind the height of a coneCone’s birthlineBody radius of a coneExercise for calculating the circumference of a cone

Before knowing the formula for calculating the surrounding area, we need to understand what a cone is.
In spatial geometry, a cone is a shape with a flat surface and an upward curved surface. The pointed end of the cone is called the top, and the flat surface is called the base.
In daily life, you can easily come across conical-shaped objects such as conical hats, ice cream cones, birthday hats, etc. It has 3 main characteristics:
One vertex is a triangle
There is 1 round side as the bottom side
Doesn’t have any edges
Formula for area around a cone
The perimeter of a cone includes the surface area around the cone, excluding the base area.
The area around the cone is equal to the product of Pi times the base radius times the cone’s generation line
Sxq = .rl
Formula to calculate area around a coneIn which:
– Sxq is the surrounding area
– is a constant, equal to 3.14
– r is the base radius
– l is the length of the birth line
Or you can use the following formula: “The area around the cone is half the product of the circumference of the base circle with the length of the birth line.” Because half the circumference of the circle is π.r.
Example: Given a cone whose base is center O and vertex A. The length of the radius from the center of the cone’s base to a base edge is 7cm, and the length of the birth line is 9cm. What is the area around the cone?
Answer: Sxq = π.rl = 3,14.7.9= 197.82 (cm)²
Refer to more Maths materials of Tran Hung Dao High School
Formulas of cones
Formula for total area of ​​a cone
The total area of ​​the cone includes both the surrounding area and the area of ​​the rounded base. Formula:
Stp = Sxq + Bottom = .rl + .r^2
Formula for volume of cone
The volume of a cone is the total amount of space it occupies, which is the product of the area of ​​the base and the height. Specifically:
V cone = .π.r^2.h
In there:
– V is the volume
– is a constant, equal to 3.14
– r is the base radius
– h is the altitude from the top to the bottom
Area around truncated cone
A truncated cone is a shape where part of the cone is cut off. The circumferential area of ​​a truncated cone includes the surrounding surface area, excluding the two base areas.
Formula for calculating the perimeter of a truncated cone
Sxq = .(r1+r2).l
Area around truncated coneIn which:
– Sxq is the surrounding area
– is a constant, equal to 3.14
– r1, r2 is the radius of 2 bases
– l is the length of the birth line
Total area of ​​truncated cone
Stp = Sxq + S 2 bottom = π.(r1+r2).l + π.(r1)^2 + π.(r2)^2
Total areaVolume of truncated cone
V = ⅓.π.h.((r1)^2 + (r2)^2 + r1.r2))
How to find the base radius, altitude, and birth line of a cone
Find the altitude of the cone
The altitude is the length from the center of the base to the top of the cone.
Formula for the height of a cone
h^2 = l^2 – r^2
Birth line of the cone
The birth line is equal to the distance from any point on the base circle to the top of the cone.
The length of the birth path of the cone
l^2 = r^2 + h^2.
length of the birth line Radius of the base of the cone
As we know, a cone is formed when we rotate a right triangle around the axis of one of its right angles. Therefore, the base radius and altitude can be considered as the two right angles of the triangle, and the birth line will be the hypotenuse. So when we know 2 of these 3 data, we can easily calculate the remaining data. Specifically:
r^2 = l^2 – h^2
Exercises to calculate the perimeter of a cone
Exercise 1: A cone has radius 4cm and height 7cm, find the perimeter of the cone.
In this exercise, first, we need to calculate the length of the birth path. The length of the birth line is calculated by the formula:
l^2 = r^2 + h^2
→ l = 8.06cm
Using the formula for the area around the cone, we have:
Sxq = .rl
= .4.8.06
= 101.23 cm2
Exercise 2: Given that the total area of ​​the cone is 375 cm. If the birth line is four times the radius, what is the diameter i.base of the jasmine cone? Use = 3
Solution instructions are as follows:
According to the topic: l = 4r and = 3
The total area of ​​the cone is 375 cm2, so we have: 3 × r × 4 r + 3 × r2 = 375
<=> 12r2 + 3r2 = 375
<=> 15r2 = 375
=> r = 5
So the radius of the base of the cone is 5 => The diameter of the cone is 5.2 = 10 cm.
Above is the formula for calculating the area around a cone and some other related formulas. According to the experience of Tran Hung Dao High School, depending on what data the question is for, you will be flexible to find the correct answer.

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