Understanding the Problem
To find the total surface area of two pieces obtained by bisecting a solid sphere, we start with the given radius of the sphere, which is 7 cm.
Calculating the Total Surface Area of One Hemisphere
When a sphere is bisected, it creates two identical hemispheres. The total surface area (TSA) of one hemisphere includes both the curved surface area and the area of the flat circular base.
Curved Surface Area of One Hemisphere
- The formula for the curved surface area (CSA) of a hemisphere is given by:
CSA = 2 * π * r^2
- For our sphere with radius r = 7 cm, the CSA becomes:
CSA = 2 * π * (7)^2
CSA = 2 * π * 49
CSA = 98π cm²
Area of the Base of the Hemisphere
- The area of the flat circular base is given by the formula:
Area = π * r^2
- For our radius:
Area = π * (7)^2
Area = 49π cm²
Total Surface Area of One Hemisphere
- Now, we add the curved surface area and the base area:
TSA of one hemisphere = CSA + Area
TSA of one hemisphere = 98π + 49π
TSA of one hemisphere = 147π cm²
Total Surface Area of Two Hemispheres
- Since we have two identical hemispheres, the total surface area of both pieces is:
Total TSA = 2 * TSA of one hemisphere
Total TSA = 2 * 147π
Total TSA = 294π cm²
Final Result
Thus, the total surface area of the two pieces obtained from bisecting the sphere is 294π cm².