Cone formulas, characteristics, properties, elements and examples of problems
Cone formulas, characteristics, properties, elements and examples of problems – How do you calculate the area and volume of a cone shape?, On this occasion About the knowledge.co.id will discuss it and of course about other things that also cover it. Let's look at the discussion together in the article below to better understand it
Cone formulas, characteristics, properties, elements and examples of problems
A spatial figure is a naming or designation for several three-dimensional shapes or shapes that have space bounded by their sides. One type of geometric shape is a cone. So a cone is one of the geometric shapes that has a circular base with a blanket that has slices of the circle.
The vertical side of the cone is an inclined plane called the conic blanket. The other side is called the base of the cone. So it can be concluded, that the cone only has 2 sides, and one edge. More details, here's a picture of the cone:
Characteristics of Cone Space
-
A cone is a pyramid-shaped geometric shape whose base is a circle.
- The cone has 2 sides.
- The cone has 1 rib.
- The cone has 1 vertex.
- Cones have a net of cones, namely circles and triangles.
Nature of Cones
-
A cone is a pyramid-shaped geometric shape whose base is a circle
- Conic nets consist of circles and triangles
- A cone has 2 sides and 1 edge
- One side is in the form of a curved plane called a conical blanket
- Has one corner point
- Has one breaking point
Cone Elements
- The base plane, namely the side that is circular (shaded area).
- The diameter of the base plane (d), that is line segment AB.
- The radius of the base plane (r), namely line OA and line segment OB.
- Cone height (t), which is the distance from the apex of the cone to the center of the base plane (line segment CO).
- Cone blanket, that is, the side of the cone that is not shaded.
- Painter's lines (s), i.e. lines on a conic blanket drawn from vertex C to points on the circle.
The relationship between r, s, and t on the cone mentioned above can be expressed by the following equations, which originate from the Pythagorean theorem, namely:
s² = r² + t²
r² = s² – t²
t² = s² – r²
Cone Netting
The following is a picture of the conical nets that the calculation formula makes. For those of you who are having trouble finding pictures of the nets to build up the space, I hope this picture can help overcome difficulties.
Conic nets consist of a circle as the base and a triangular shape with a curved base as the blanket.
Cone Formula
-
Cone Volume Formula
V = 1/3πr².t
Basically a cone is a pyramid because it has a vertex so that the volume of the cone is equal to the volume of the pyramid, ie 1/3 times the area of the base times the height. Since the base of the cone is circular, the area of the base is the area of the circle. Thus, the volume of a cone can be formulated as follows.
with
r = radius of the base circle
t = cone height
Because r = 1/2 d (d is the diameter of the circle) then another form of the volume formula of a cone is as follows.
Problems example:
Cone Surface Area Formula
We need to know that the surface of a cone consists of two planes, namely a curved plane (blanket) and a circular base plane. For more details, consider the following description.
L = Circle Area + Blanket Area
L = πr²+ trs or
L = πr. (r+s)
with:
r: radius of the base circle
s: apothem
π = 22/7 or 3.14
Example of a Cone Surface Area Problem:
- A cone has a radius of base 6 cm and a height of 8 cm. Calculate the surface area of the cone ( π = 3.14).
Answer :
Is known:
Base radius = r = 6cm
Cone height = t = 8 cm
Wanted: Surface area of a cone
Completion:
-
Area of a Cone Base
L = πr²
-
Cone Blanket Area Formula
L = πrs
Information:
r = radius (cm)
H = height (cm)
π = 22/7 or 3.14
- Area of the Truncated Cone
The area of the large cone minus the area of the small cone.
So
-
Area of a Cone
Example :
Answer :
Example of Cone Space Problems
Problem 1.
A circle has an area of 40 cm². If the circle is turned into a cone with a height of 9 cm, find the volume of the cone.
Answer:
Is known:
t = 9 cm
Area: L = π x r² = 40 cm²
V = 1/3 x π x r² x t
= 1/3 x 40 x 9 (remember: π x r² = 40 cm²)
= 120 cm³.
So, the volume of the cone is 120 cm³.
Problem 2
If the diameter of a cone is 10 cm and its height is 12 cm, determine:
a. apothem length(s),
b. conical blanket area,
c. surface area
Answer:
Is known :
d = 10 then r = 5 cm
t = 12 cm
Asked:
a. painter line length(s)
b. area of the cone blanket
c. cone surface area
Completion:
- a. s2 = t2 +r2
= 122 + 52
= 144 + 25
= 169
So, the length of the conical line is 13 cm.
- b. Conic area = πrs
= 3.14 x 5 x 13
= 204,1
So, the area of the cone is 204.1 cm2.
- c. Surface area of cone = πr (s + r)
= 3.14 x 5 x (13 + 5)
= 282,6
So, the surface area of the cone is 282.6 cm2
Problem 3
Consider a cone with a height of 8 cm. If the radius is 16 cm, what is the volume of the shape?
V = 1/3πr². t
V = 1/3 x 22/7 x 16 x 16 x 8
V = 2.124 cm³
Problem 4
A cone has a height of 16 cm. If the radius of the cone is 10 cm, what is the volume of the shape? (π = 3,14)
V = 1/3 x 3.14 x 10 x 10 x 16 = 1657 cm³
Problem 5
It is known that a cone has a volume of 8,300 cm³. Find the diameter of the cone if its height is 20 cm! (π = 22/7)
V = 1/3πr².t
8,300 = 1/3 x 22/7 x r² x 20
8,300 = 147/7 x r²
r² = 8.316 x 7/147
r² = 396
r = √396
r = 19.9 cm
So:
d = 2r
d = 2 x 19.9
d = 39.8 cm
Problem 6
A cone has a base radius of 6 cm and a height of 8 cm. What is the area of the cone ( π = 3.14).
Answer :
r = 6cm
t = 8 cm
s² = r² + t²
s² = 6²+ 8² = 36 + 64 = 100
s =√100 = 10
Area of the cone = πr (r + s)
= 3.14 x 6 x (6 + 10) = 3.14 x 6 x l6 = 301.44
So, the side area of the cone is 301.44 cm²
Problem 7.
A birthday hat has the shape of a cone with a radius of 28 cm and a height of 10 cm, what is the volume of the hat?
Answer :
r = 28 cm
t = 10 cm
V = x base area x height
V = x πr2 x t
V = πr2t
V = x x 282 x 10 cm
V = 8213.3 cm³
Thus the review from About the knowledge.co.id about Cone formulas, characteristics, properties, elements and examples of problems, hopefully can add to your insight and knowledge. Thank you for visiting and don't forget to read other articles.
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