A solid sphere has a surface area of 616cm
2
. This sphere is now cut into two hemispheres. What is the total surface area of one of the hemispheres?
- A440 cm²
- B462 cm²
- C452 cm²
- D390 cm²
Solution & Step-by-step Explanation
Let the radius of the sphere be r.
The surface area of a solid sphere is given by: 4πr
2
=616cm
2
Dividing by 2, we get the curved surface area of a hemisphere: 2πr
2
=308cm
2
The total surface area (TSA) of a solid hemisphere includes its curved surface area and the base flat circular area:
TSA of hemisphere=3πr
2
Since 4πr
2
=616:
πr
2
=
4
616
=154cm
2
Therefore:
TSA of hemisphere=3×154=462cm
2
The surface area of a solid sphere is given by: 4πr
2
=616cm
2
Dividing by 2, we get the curved surface area of a hemisphere: 2πr
2
=308cm
2
The total surface area (TSA) of a solid hemisphere includes its curved surface area and the base flat circular area:
TSA of hemisphere=3πr
2
Since 4πr
2
=616:
πr
2
=
4
616
=154cm
2
Therefore:
TSA of hemisphere=3×154=462cm
2