how do you find the surface are of a cone whose radius is 10cm and height 24 cm.
To find the surface area of a cone, you need to calculate the area of the curved surface (lateral surface area) and add it to the area of the base.
1. Lateral Surface Area (A_ls):
The lateral surface area of a cone can be found using the formula A_ls = πrℓ, where r is the radius and ℓ is the slant height of the cone.
To calculate ℓ, we can use the Pythagorean theorem. Since the slant height, height, and radius form a right triangle, we have ℓ = √(r^2 + h^2).
Given:
- Radius (r) = 10 cm
- Height (h) = 24 cm
First, calculate the slant height (ℓ):
ℓ = √(10^2 + 24^2)
Now, plug in the values of ℓ and r into the area formula:
A_ls = π * 10 * ℓ
2. Base Area (A_b):
The base area of a cone is found using the formula A_b = πr^2.
Given:
- Radius (r) = 10 cm
Calculate the base area:
A_b = π * 10^2
3. Total Surface Area (A_total):
To find the total surface area, add the lateral surface area (A_ls) to the base area (A_b):
A_total = A_ls + A_b
Now, plug in the calculated values of A_ls and A_b into the formula:
A_total = A_ls + A_b
After performing the calculations, you will get the value for the total surface area of the cone.