To find the surface area, we must first find the radius.  Based on our description, this passes from (0,0) to (6,8).  This can be found using the distance formula:

6² + 8² = r²; r² = 36 + 64; r² = 100; r = 10

It should be noted that you could have quickly figured this out by seeing that (6,8) is the hypotenuse of a 6-8-10 triangle (which is a multiple of the "easy" 3-4-5).

The rest is easy.  The surface area of the sphere is defined by:

A = 4πr² = 4 * 100 * π = 400π

To begin, we must determine the dimensions of the cube. To do this, recall that the surface area of a cube is made up of six squares and is thus defined as: A = 6s², where s is one of the sides of the cube. For our data, this gives us:

726 = 6s²; 121 = s²; s = 11

Now, if the sphere is contained within the cube, that means that 11 represents the diameter of the sphere. Therefore, the radius of the sphere is 5.5 units. The surface area of a sphere is defined as: A = 4πr². For our data, that would be:

A = 4π * 5.5² = 30.25 * 4 * π = 121π

The surface area of a sphere is 4πr². The area of a circle is πr². 16/16 is equal to 1.

Let's call the radius of the sphere r. The formula for the surface area of a sphere (A) is given below:

A = 4πr²

Because the sphere is inscribed inside the cube, the diameter of the sphere is equal to the side length of the cube. Because the diameter is twice the length of the radius, the diameter of the sphere is 2r. This means that the side length of the cube is also 2r. 

The surface area for a cube is given by the following formula, where s represents the length of each side of the cube:

surface area of cube = 6s²

The formula for surface area of a cube comes from the fact that each face of the cube has an area of s², and there are 6 faces total on a cube. 

Since we already determined that the side length of the cube is the same as 2r, we can replace s with 2r.

surface area of cube = 6(2r)² = 6(2r)(2r) = 24r².

We are asked to find the ratio of the surface area of the cube to the surface area of the sphere. This means we must divide the surface area of the cube by the surface area of the sphere.

ratio = (24r²)/(4πr²)

The r² term cancels in the numerator and denominator. Also, 24/4 simplifes to 6.

ratio = (24r²)/(4πr²) = 6/π

The answer is 6/π.

A hemisphere is half of a sphere.  The surface area is broken into two parts:  the spherical part and the circular base. 

The surface area of a sphere is given by .

So the surface area of the spherical part of a hemisphere is . 

The area of the circular base is given by .  The radius to use is half the diameter, or 2 cm.

Write the surface area formula for a sphere.

Substitute the value of the radius.

Write the formula for the surface area of a cube.

Substitute the length.

Write the formula for the surface area of a cube.

Substitute the side length into the equation.

Simplify the square inside the parentheses and multiply.

To solve, simply use the following formula for the surface area of a cube.

Thus,

A cube has  sides that have equal length edges and also equal side areas.  

To find the total surface area, you just need to multiple the side area () by  which is,

.