find the total surface area where a cone has a height of 16cm and the diameter of the base is 24
http://math.about.com/od/formulas/ss/surfaceareavol_2.htm
You will have to calculate slant height:
s= sqrt(r^2+h^2)
To find the total surface area of a cone, you need to add the lateral surface area (the curved part) to the base area.
First, let's calculate the slant height of the cone using the given information. The slant height (l) can be found using the Pythagorean theorem:
l² = r² + h²
where r is the radius of the base and h is the height of the cone.
Since the diameter (d) is given as 24 cm, the radius (r) is half of that: r = d/2 = 24/2 = 12 cm.
Now we can calculate the slant height (l):
l² = 12² + 16²
l² = 144 + 256
l² = 400
l = √400
l = 20 cm
Next, we can calculate the lateral surface area (A_lateral) of the cone using the formula:
A_lateral = π * r * l
Substituting the values, we have:
A_lateral = π * 12 * 20
A_lateral = 240π cm²
Now, let's calculate the base area (A_base) of the cone using the formula:
A_base = π * r²
Substituting the radius, we get:
A_base = π * (12)²
A_base = 144π cm²
Lastly, we can find the total surface area (A_total) by adding the lateral surface area and the base area together:
A_total = A_lateral + A_base
A_total = 240π + 144π
A_total = 384π cm² (approximately 1208.96 cm², when using the value of π as 3.14)
Therefore, the total surface area of the cone is approximately 1208.96 cm².