Surface Area of Cube & Inscribed Sphere

Thread starter jean-paul
Start date Aug 21, 2013
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Area Cube Surface Surface area

In summary, the surface area of a cube can be found by multiplying 6 by the length of one side squared. If the length of one side is not given, it can be calculated by taking the cube root of the volume of the cube. An inscribed sphere is a sphere that fits perfectly inside a cube, and its surface area can be found using the formula 4πr², where r is the radius of the sphere. However, the surface area of a cube will always be greater than the surface area of an inscribed sphere as the corners of the cube are not included in the surface area of the sphere.

Aug 21, 2013

jean-paul

Is there any relationship between the surface area of a cube and the surface area of the cube's inscribed sphere?

Jean~

Last edited: Aug 21, 2013

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Aug 21, 2013

phinds

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If you write the equation for each in terms of the radius of the inscribed cube, you'll be able to get a relationship between the two. It's trivially easy.

Last edited: Aug 21, 2013

1. What is the formula for finding the surface area of a cube?

The formula for finding the surface area of a cube is 6 times the length of one side squared. This can also be written as 6s², where s represents the length of one side.

2. How do you find the surface area of a cube if the length of one side is not given?

If the length of one side is not given, you can find it by taking the cube root of the volume of the cube. Once you have the length of one side, you can use the formula 6s² to find the surface area.

3. What is an inscribed sphere?

An inscribed sphere is a sphere that is enclosed within a cube, where the sphere's center lies at the center of the cube and its surface touches all six faces of the cube.

4. How do you find the surface area of an inscribed sphere in a cube?

The surface area of an inscribed sphere in a cube can be found by using the formula 4πr², where r is the radius of the sphere. The radius of the sphere can be found by dividing the length of one side of the cube by 2.

5. Can the surface area of a cube and the surface area of an inscribed sphere be equal?

No, the surface area of a cube and the surface area of an inscribed sphere cannot be equal. The surface area of a cube will always be greater than the surface area of an inscribed sphere, as the corners of the cube are not included in the surface area of the inscribed sphere.