Choose the correct answers to the questions from the given options. A solid sphere is cut into two identical hemispheres. Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere. Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere. Which of the following is valid?
Explanation
The volume of a sphere = (4/3) * pi * r^3. The volume of a hemisphere = (2/3) * pi * r^3. Therefore, the total volume of two hemispheres is equal to the volume of the original sphere. The surface area of a sphere = 4 * pi * r^2. The surface area of a hemisphere = 3 * pi * r^2. Therefore, the total surface area of two hemispheres together is equal to the surface area of the original sphere. Hence, both the statements are true.
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