A hemisphere has a curved surface area that is equal to half the surface area of a sphere with the same radius.
The formula for the curved surface area of a hemisphere is:
A = 2πr^2
where A is the curved surface area and r is the radius of the hemisphere.
To find the area of the base of the hemisphere, we need to know the total surface area of the hemisphere. The formula for the total surface area of a hemisphere is:
A = 3πr^2
Since we know that the curved surface area of the hemisphere is half the surface area of a sphere with the same radius, we can write:
A = (1/2)(4πr^2)
Simplifying this expression, we get:
A = 2πr^2
This is the same formula that we had for the curved surface area of the hemisphere.
Therefore, we cannot determine the area of the base of the hemisphere from the given information.
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Verified answer
[tex] \star \boxed{\sf{} \:Base \: area = \: \dfrac{A}{2}} \star[/tex]
Explanation:
As we know that ;
Total Surface Area of Hemisphere is equals to the sum of curved surface area of hemisphere and Base area .Therefore ;
[tex] \sf{}TSA = 2\pi {r}^{2} + \pi {r}^{2} \\ \\ \sf{}TSA = 3\pi {r}^{2} [/tex]
Now , it is given that curved surface area of hemisphere is equals to A .
[tex] \implies \sf{}CSA = A \\ \\ \implies\sf{}2\pi {r}^{2} = A[/tex]
Now , we know that Base area of hemisphere is half of the curved surface area .Therefore
By dividing both sides by 2
[tex] \sf{} \rightarrow \frac{2\pi {r}^{2} }{2} = \dfrac{A}{2} \\ \\ \rightarrow \sf{}\pi {r}^{2} = \dfrac{A}{2}[/tex]
Therefore , If curved surface area of hemisphere is equals to A .Then the base are would be A/2
Answer:
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Step-by-step explanation:
A hemisphere has a curved surface area that is equal to half the surface area of a sphere with the same radius.
The formula for the curved surface area of a hemisphere is:
A = 2πr^2
where A is the curved surface area and r is the radius of the hemisphere.
To find the area of the base of the hemisphere, we need to know the total surface area of the hemisphere. The formula for the total surface area of a hemisphere is:
A = 3πr^2
Since we know that the curved surface area of the hemisphere is half the surface area of a sphere with the same radius, we can write:
A = (1/2)(4πr^2)
Simplifying this expression, we get:
A = 2πr^2
This is the same formula that we had for the curved surface area of the hemisphere.
Therefore, we cannot determine the area of the base of the hemisphere from the given information.