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Common Core Standard 8.G.9
H
A
B
Oblique Cone
Right Cone
Click on the picture for a helpful area and volume of a cone calculator.
The calculator will find the area along with the radius,height, or slant height of the cone when given two values.
The calculator will also calculate the volume of the cone.
Truncated Cone
A truncated cone is a solid similar to a cylinder, except that the circular bases are not equal in size. You could describe the shape like a lamp shade.
Think of it as a cone with the portion containing the vertex removed.
If the cut is parallel to the base then it is a frustum of a cone.
The surface area of a truncated cone
π(B+A)*square root [ (A- B)^2 + H^2 ] + π(B^2 + A^2)
In summary... To find the surface area of a cone follow these steps.
- Find the lateral area of a cone using:
- πradius x slant height of the cone
- Find the base area of the cone using:
- πradius squared
- Add the Lateral area plus the base area
What is a cone in geometry?
A cone is a three-dimensional geometric shape. The base of a cone is circular in shape.
A cone has only one vertex.
Two common types of cones are the right cone and the oblique cone
A right cone has its apex positioned over the cones center of the base.
The apex of a oblique cone is not positioned over the center of the cone's base
Area =lateral area of the cone + base area of the cone
Combine these for the surface area formula = πr*s + πr2
r = radius s = slant height
Slant height equals =√h2 +r2
h = height r = radius
Surface Area of a Cone Example Problem
Find the surface area of a cone with a height of 8 and a radius of 6
Step 1: Find the lateral area of the cone.
Step 1a: Find the slant height using Pythagorean Theorem
6^2+8^2= C^2
36 + 64 = √100=10 Slant height
Step 1b: Using the slant height, s, to plug into the lateral area formula:
πr*s, where r = 6 and s=10
π*6 *10=60 π
Step 2: Find the area of the base of the cone
Formula: πr^2 where r = 6
π6^2= π*36 or 36π
Step 3: Add lateral area (step 1) and add base area (step 2) together for the total surface area
Formula: πr*s+ πr^2
60 π + 36π=96π units squared
Area of a Cone
h
r
Slant Height = s
6
8
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Area of a Cone Video
- Step by step directions for the surface area of a cone
- Formula for finding surface area of a cone
- Definition of slant height
- How to find lateral area
- How to find base area
The surface area of a cone is the outside covering of the cone. Finding the surface area of a cone involves finding the lateral area and adding this to the base area of the cone.