Find the radius of a cone if the total area = 12 pi and lateral area = 8 pi.
If the total area is 12π and the lateral area is 8π, then the area of the circular base must be 5π
πr^2 = 5π
r^2 = 5
r = √5
To find the radius of a cone, we need to know the total surface area and the lateral surface area of the cone.
The total surface area of a cone is given by the formula:
Total Surface Area = Base Area + Lateral Surface Area
We are given that the total surface area is 12π and the lateral surface area is 8π.
Substituting these values into the formula, we have:
12π = Base Area + 8π
To find the base area, we need to subtract the lateral surface area from the total surface area:
Base Area = Total Surface Area - Lateral Surface Area
= 12π - 8π
= 4π
The base area of the cone is 4π.
The base area of a cone is given by the formula:
Base Area = π * radius^2
Substituting the given base area into the formula, we have:
4π = π * radius^2
To find the radius, we can divide both sides of the equation by π and then take the square root:
radius^2 = 4
radius = √4
radius = 2
Therefore, the radius of the cone is 2.