A cone has a height of #27 cm# and its base has a radius of #12 cm#. If the cone is horizontally cut into two segments #8 cm# from the base, what would the surface area of the bottom segment be?
1 Answer
Explanation:
When we cut a right circular cone horizontally in two segments as in the problem, we end up with
- A small cone (top part),
- Frustum (bottom part).
as shown in the above figure
The curved area of the frustum is given by the expression
Curved area of the frustum
Area of the top circular face
Area of the bottom circular face
From the figure
To obtain
or
Inserting given values in (1) above we obtain
Total surface area of the frustum
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-..-
Alternatively
We know that area of Curved surface of a right circular cone
We can use this formula to calculate the curved surface of frustum
Curved surface of frustum
Curved Surface of Larger Cone