AB= ft2
CB = ft
l (slant height) = ft
S = ft2
I need to find the answers this is a cone with a radius of 5 and a height of 13. Thank you
To find the values of AB, CB, l, and S for the given cone with a radius of 5 and a height of 13, we will use the formulas related to cone geometry.
First, let's find AB, the area of the base of the cone.
The formula to calculate the area of a circle is:
A = π * r^2
Where A is the area and r is the radius.
Plugging in the given radius of 5, we get:
A = π * (5)^2 = π * 25 = 25π ft^2
So, AB = 25π ft^2
Next, let's find CB, the circumference of the base of the cone.
The formula to calculate the circumference of a circle is:
C = 2 * π * r
Plugging in the given radius of 5, we get:
C = 2 * π * 5 = 10π ft
So, CB = 10π ft
Now, let's find l, the slant height of the cone.
The formula to calculate the slant height of a cone is:
l = √(r^2 + h^2)
Where r is the radius and h is the height.
Plugging in the given radius of 5 and height of 13, we get:
l = √(5^2 + 13^2) = √(25 + 169) = √194 = approximately 13.928 ft
So, l ≈ 13.928 ft
Finally, let's find S, the lateral surface area of the cone.
The formula to calculate the lateral surface area of a cone is:
S = π * r * l
Plugging in the given radius of 5 and slant height of 13.928, we get:
S = π * 5 * 13.928 ft^2 = 69.64π ft^2 ≈ 218.102 ft^2
So, S ≈ 218.102 ft^2
Therefore, the answers for the given cone are:
AB = 25π ft^2,
CB = 10π ft,
l ≈ 13.928 ft,
S ≈ 218.102 ft^2