Total Surface Area of Two Halved Spheres
When a solid sphere is bisected, it results in two hemispheres. The total surface area of these two pieces includes the curved surface area and the area of the flat circular bases created by the bisection.
1. Understanding the Components
- Curved Surface Area of One Hemisphere: This is given by the formula 2 * π * r².
- Area of the Circular Base: The area of the circular base of one hemisphere is calculated using the formula π * r².
2. Total Surface Area of One Hemisphere
- The total surface area of one hemisphere includes its curved surface area and the base:
- Total Surface Area of One Hemisphere = Curved Surface Area + Area of Base
- Total Surface Area of One Hemisphere = 2 * π * r² + π * r²
- Thus, Total Surface Area of One Hemisphere = 3 * π * r².
3. Total Surface Area of Two Hemispheres
- To find the total surface area of both hemispheres:
- Total Surface Area of Two Hemispheres = 2 * (3 * π * r²)
- Therefore, Total Surface Area of Two Hemispheres = 6 * π * r².
4. Conclusion
- The total surface area of the two pieces obtained after bisecting a solid sphere of radius 'r' centimetres is 6 * π * r².
- This provides a comprehensive measure of the exposed surfaces of both hemispheres, considering their curved and flat areas.
In summary, the process effectively demonstrates how geometry can reveal the properties of shapes when altered.