1. Surface Area of a Cone:
Formula:
To find the surface area of a cone, we use this formula:
A = π r (r + l)
Here, r is the radius, and l is the slant height.
Example:
Imagine a cone with a radius of 3 and a slant height of 5.
Let's figure out the surface area:
[ A = π (3)(3 + 5) = π (3)(8) = 24π \approx 75.4 \text{ square units} ]
So, the surface area of this cone is about 75.4 square units.
2. Volume of a Cone:
Formula:
To calculate the volume of a cone, we use this formula:
V = (1/3) π r² h
In this case, h is the height of the cone.
Example:
Let’s say our cone has a radius of 3 and a height of 5.
We can calculate the volume like this:
[ V = (1/3) π (3)² (5) = (1/3) π (9)(5) = 15π \approx 47.1 \text{ cubic units} ]
So, the volume of this cone is about 47.1 cubic units.
Comparison with a Cylinder:
If we have a cylinder that has the same radius and height as our cone, the cone’s volume is one-third of the cylinder's volume.
This shows us how the cone is great at saving space!
1. Surface Area of a Cone:
Formula:
To find the surface area of a cone, we use this formula:
A = π r (r + l)
Here, r is the radius, and l is the slant height.
Example:
Imagine a cone with a radius of 3 and a slant height of 5.
Let's figure out the surface area:
[ A = π (3)(3 + 5) = π (3)(8) = 24π \approx 75.4 \text{ square units} ]
So, the surface area of this cone is about 75.4 square units.
2. Volume of a Cone:
Formula:
To calculate the volume of a cone, we use this formula:
V = (1/3) π r² h
In this case, h is the height of the cone.
Example:
Let’s say our cone has a radius of 3 and a height of 5.
We can calculate the volume like this:
[ V = (1/3) π (3)² (5) = (1/3) π (9)(5) = 15π \approx 47.1 \text{ cubic units} ]
So, the volume of this cone is about 47.1 cubic units.
Comparison with a Cylinder:
If we have a cylinder that has the same radius and height as our cone, the cone’s volume is one-third of the cylinder's volume.
This shows us how the cone is great at saving space!