Cone Surface Area Formulas and Volume Formulas along with Example Problems
Cone Surface Area – It is calculated by adding the area of the base to the area of the blanket. Cone blankets are the sides of an upright and curved surface. The following is a complete explanation of the formula for the surface area of a cone along with formulas related to cones. For more details, see the discussion below
Table of contents :
Definition of Cones
A cone is a pyramid with a circular base. The cone shape is the most common geometry. Examples of cone-shaped objects are rice cones, birthday hats, ice cream cones, and so on. A cone has two surfaces, namely a blanket and a base.
Look at the following picture
The image below to understand more about cones is a picture of a cone (figure i) and conical nets (figure ii). t is the height of the cone, r is the radius and s is the painter's line on the cone.
Cone Surface Area Formula
How to find the surface area of a cone by adding the area of the base to the area of the blanket.
Cone Surface Area = Base Area + Blanket Area
= ·r2 + ·r·s
= ·r · (r + s)
The area of the base of a cone has the shape of a circle so that it can be calculated by the formula L = r2. The area of a conical blanket can be calculated by the formula L = rs, Where s i.e. the length of the conical painter's line.
Cone Volume Formula
The volume of a cone can basically be calculated by the formula for the volume of a pyramid, because it is necessary to know the surface area and height of the cone:
Volume of Cone = 1/3 Area of Base Height
The area of the base is calculated by the formula for the area of a circle, which is r2. with r is the radius of the circle and π namely a constant with an approximate value of 22/7. Until the formula is obtained:
Volume of Cone = 1/3 · · r2 · t
Example Problems Calculating the Surface Area of a Cone
Here are some examples of calculating the area of a cone blanket and the surface area of a cone.
Example Question 1
Find the surface area of a cone whose radius is 21 cm and the length of the painter's line is 40 cm.
Answer:
The radius, r is 21 cm
Painter's line, s is 40 cm
The formula for the area of the blanket = .r.s
= (22/7).(21).(40) = 2.640
Then the area of the cone blanket is 2.640 cm2.
Example Question 2
What is the surface area of a cone with a diameter of 14 cm and a painter's line 15 cm?
Answer:
Radius, r is 14/2 = 7 cm
Painter's line, s is 15 cm
The formula for the surface area of a cone = .r (r + s)
= (22/7).(7).(7+15) = 484
Then the surface area of the cone is 484 cm2.
Example Question 3
A farmer's hat has the shape of a cone with a base radius of 6 cm and a height of 8 cm. Calculate the surface area of the hat if the value of is 3.14!
Is known
r is 6 cm
t is 8 cm
s is (6^2+8^2 )
= √(36+64)
= 100 = 10 cm
The formula for the surface area of a cone is r (r+s)
= 3,14 ×6 (6+10)
= 3,14 ×6 (6+10)
= 3,14 ×6 ×16
= 301,44
So, the surface area of the hat is 301.44 cm^2
Example Question 4
The area of the Cone Blanket with the painter's line length is 25 cm, which is 1,570 cm^2. Calculate: The radius of the base of the cone and the surface area of the cone ?
Answer:
The formula for the area of a cone blanket = rs
1,570 cm^2 = 22/7 × r × 25
1,570 cm^2 = (22×25) / 7 × r
1,570 cm^2 = 550/7 × r
r = (1,570 ×7)/550
r= 19.98 cm or 20 cm
Cone Surface Area Formula = r (r+s)
= 22/7 × 20 × (20+25)
= 22/7 × 20 × 45
= 2828 cm2
That's an explanation of the surface area of a cone along with an example of the problem, Hopefully it's useful
Other Articles:
- The formula for the surface area of the cuboid, the area of the base, the area of the sides and examples of the problem
- The formula for the surface area of a cylinder, the area of the base, the area of the blanket, the volume and examples of problems
- Chemical Changes: Characteristics, Examples, and Definition
- Physical Changes: Characteristics, Definition, and Complete Examples
2/5(1 vote )