How to calculate dA of a hemisphere.

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In summary, the conversation is discussing the differences between dA and dV and how boundaries for integrations are determined. It is explained that dS is the infinitesimal area element of a sphere and its direction is radial, which is why there is a component for v_r. dS can be divided into two parts, with the first part being the base of the rectangular area and the second part being the height.
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dS is the infinitesimal area element of a sphere in this case. It is given by
[tex]dS=R^2\sin{\theta}d\theta d\phi [/tex]

Its direction is radial, that's why you have the component [tex]v_r[/tex] in the second step.

[tex] dS [/tex] can be thought of as 2 parts. The first part is [tex] R\sin{\theta}d\phi [/tex], which can be thought of as the base of the rectangular area. The second part is [tex] R d\theta [/tex], which is the height of the rectangular area.
 

Related to How to calculate dA of a hemisphere.

1. What is the formula for calculating the surface area of a hemisphere?

The formula for calculating the surface area of a hemisphere is 2πr2, where r is the radius of the hemisphere.

2. How do you find the radius of a hemisphere?

The radius of a hemisphere can be found by dividing the diameter of the hemisphere by 2.

3. Are there any other methods for calculating the surface area of a hemisphere?

Yes, you can also use the formula π2 + 2πr2 to calculate the surface area of a hemisphere.

4. How is the surface area of a hemisphere related to its volume?

The surface area of a hemisphere is directly proportional to its volume. As the volume increases, the surface area also increases.

5. Can the formula for calculating the surface area of a hemisphere be used for other shapes?

No, the formula for calculating the surface area of a hemisphere is specific to a hemisphere shape. Other shapes have their own formulas for calculating surface area.

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