Question
Why is the surface area of a hemisphere with a radius of 10m with the answer in terms of pi, the correct answer 300π m^2 and NOT 200π m^2?
Answers
Answered by
GPT 3.5
The surface area of a hemisphere is calculated by finding the sum of the areas of its curved surface and its circular base.
The curved surface area of a hemisphere can be found by calculating half of the surface area of a sphere. The surface area of a sphere is given by the formula 4πr^2, where r is the radius. Therefore, the surface area of the curved surface of a hemisphere with a radius of 10m is 1/2 * 4π(10^2) = 200π m^2.
In addition to the curved surface, the hemisphere also has a circular base. The area of a circle is given by the formula πr^2, where r is the radius. The radius of the circular base of the hemisphere is also 10m, so the area of the circular base is π(10^2) = 100π m^2.
To find the total surface area of the hemisphere, we add the curved surface area and the base area: 200π m^2 + 100π m^2 = 300π m^2.
Therefore, the correct answer is 300π m^2, not 200π m^2, because we need to consider both the curved surface area and the base area of the hemisphere.
The curved surface area of a hemisphere can be found by calculating half of the surface area of a sphere. The surface area of a sphere is given by the formula 4πr^2, where r is the radius. Therefore, the surface area of the curved surface of a hemisphere with a radius of 10m is 1/2 * 4π(10^2) = 200π m^2.
In addition to the curved surface, the hemisphere also has a circular base. The area of a circle is given by the formula πr^2, where r is the radius. The radius of the circular base of the hemisphere is also 10m, so the area of the circular base is π(10^2) = 100π m^2.
To find the total surface area of the hemisphere, we add the curved surface area and the base area: 200π m^2 + 100π m^2 = 300π m^2.
Therefore, the correct answer is 300π m^2, not 200π m^2, because we need to consider both the curved surface area and the base area of the hemisphere.
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