if a cone is cut through the centre where it makes perpendicular to the vertex.what will be the surface area of the obtained half the cone
please any concept or formula for the previous question,i stuck
The curved part (and maybe the base) is just half the surface area of the cone, for which I'm sure you have the formula.
The interior which is exposed is just a triangle. Its area is also easy to find.
To find the surface area of the obtained half cone, we first need to find the slant height of the cone.
The slant height can be calculated using the Pythagorean theorem. Let's assume the radius of the original cone is 'r' and the height of the cone is 'h'. Since the cut is made through the center and perpendicular to the vertex, we obtain a half cone with radius 'r' and height 'h/2'.
To find the slant height 'l', we can use the formula:
l² = r² + (h/2)²
Once we have the slant height, we can calculate the surface area of the half cone.
The surface area of a cone formula is:
A = πr(r + l)
Now, substituting the values, we get:
A = πr(r + √(r² + (h/2)²))
Therefore, the surface area of the obtained half cone is given by the formula above.