Cone Blanket Area Formula and Example Problems Contoh
Cone Blanket Area – a space whose one side has the shape of a circle is a cone. A cone is a shape that consists of 2 sides. One side becomes a circular base and the other side is curved which is often referred to as a conical blanket. Here's how to calculate the area of a conical blanket along with an example problem
Table of contents :
Definition of Cones
This shape has 1 curved edge and 1 corner point.
The area of the cone is the sum of the area of the base of the cone and the area of the blanket of the cone. Below is a brief summary of the formula for the area of a cone and an example of the problem.
Cone area formula
The cone consists of a base and a blanket. The base of the cone has the shape of a circle, so the formula for the area of the base of the cone is
r²
A blanket cone is a curved plane that has the formula
x r x s.
The formula for the area of a cone (surface area of a cone) is =
area of base of cone + area of blanket of cone
= r² + rs
= r(r+s)
So, the area of the cone is:
Area of the cone = r ( r + s)
Formula Description:
r is the radius of the base of the cone
s is the painter's line ==> s = (r² + t²)
t is the height of the cone
Look at the picture below
If the cone in the figure above is split along the line between C and D, and the circumference of the base can be obtained from the net of the cones as shown in the figure below.
The conical nets in the picture above consist of:
- CDD' circle is a blanket of cones
- The circle of radius r is the side of the base of the cone
Look again at the picture above, it can be seen if the length of the radius of the circle is equal to S. Meanwhile, the arc length DD' is equal to the circumference of the base of the cone, which is 2πr. It can be stated that, the area of the blanket of the cone is equal to the area of the CDD'.
Problems example :
Example Question 1
Rangga made a hat with a cone shape out of cardboard. If Rangga wants to make a hat that is 16 cm high and the diameter of the base is 24 cm. How much area of cardboard does Ragg need?
Answer:
The conical hat, of course, has no base. So, what you are looking for is the area of the cone blanket.
the diameter of the base is 24 cm,
then the radius is 24: 2 = 12 cm
r = 12 cm
t = 16 cm
painter's line: s = (r² + t²)
= √( 12² + 16² )
= √( 144 + 256 )
= √400 = 20
= 20 cm
Area of blanket of cone = x r x s
= 3,14. 12. 20
= 753,6
So, the area of cardboard needed by Rangga is 753.6 cm²
Example Question 2
A cone has a base with a diameter of 20 cm and a height of 24 cm. What is the total surface area of the cone?
Answer:
the diameter of the base = 20 cm
then the radius is 20: 2 = 10 cm
r = 10 cm
t = 24 cm
painter's line: s= (r² + t²)
s = ( 10² + 24² )
= √( 100 + 576 )
= √676
= 26 cm
Cone surface area = r(s + r)
= 3,14. 10 ( 26 + 10 )
= 3,14. 10. 36
= 1,130.4 cm²
So, the surface area of the cone is 1130.4 cm².
Example Question 3
The cone is made of a sheet of zinc which has the shape of a semi-circle with a radius of 42 cm. What is the radius of the base of the cone?
Answer:
is known :
a sheet of zinc in the shape of a semicircle is 180º. (Measurement of the angle of a circle is 360º. Since the cone is formed from a semi-circle, the measure of the angle is 180º).
the radius of zinc is the painter's line (s) = R = 42 cm,
then the circumference of the base of the cone (2πr) = arc length (measurement of the angle of the semicircle/360º x 2πR)
2πr = 2πR
r = 180º/360º x 42
= 1/2 x 42
= 21 cm
Therefore, the radius of the base of the cone is 21 cm.
Thus the discussion about the formula for the area of a cone blanket
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