# Why Do Sphere Surface Areas Differ With Same Approximation?

• joseph_seb
In summary, the speaker found two different answers for the area of a sphere using two different methods with the same approximation. They then asked how this could happen and attached a solution for reference. The expert summarizer notes that the mistake lies in assuming the frustum is equal to the cylinder, and provides two links for further explanation. The expert also questions the extra sin(theta) in the speaker's calculations.
joseph_seb
i have found the area of sphere in two ways using the same approximation.but i get two different answers ;one the correct value 4∏R^2?how does this happen?
i'm attaching the solution below?please refer to the attachments and give a solution?

#### Attachments

• spherearea1.jpg
20.3 KB · Views: 508
• spherearea2.jpg
17.1 KB · Views: 480

Your mistake is where "transform the frustrum to a cylinder". You don't actually do a "tranformation" you just assume frustrum is equal to the cylinder and that is not true.

You write dA = 2Pirh and h = rsin(theta)dtheta, but then you write dA = 2Pir^2 sin^2(theta) dtheta. Where does the extra sin(theta) come from?

## 1. Why do spheres have different surface areas when they have the same approximation?

The surface area of a sphere is determined by its radius, not its approximation. Even with the same approximation, if the radii of two spheres are different, their surface areas will also be different.

## 2. Can two spheres with the same radius have different surface areas?

No, if two spheres have the same radius, they will have the same surface area. The radius is the only factor that affects the surface area of a sphere.

## 3. How does the approximation of a sphere affect its surface area?

The approximation of a sphere does not directly affect its surface area. However, using a smaller approximation can result in a closer estimation of the actual surface area of the sphere.

## 4. What is the formula for calculating the surface area of a sphere?

The formula for calculating the surface area of a sphere is 4πr^2, where r is the radius of the sphere.

## 5. Can the surface area of a sphere be larger than the circumference?

No, the surface area of a sphere cannot be larger than its circumference. The circumference of a sphere is a one-dimensional measure, while the surface area is a two-dimensional measure.

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