Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

Plug in the given radius to find the volume.

Next, recall how to find the volume of a cube:

Plug in the given side length to find the volume of the cube.

Finally, subtract the volume of the sphere from the volume of the cube.

Make sure to round to  places after the decimal.

Let  be the length of one side of the cube. Then the base of the pyramid is a right triangle with legs of length . The area of a right triangle is half the product of the lengths of the legs, so the base has area

The volume of a pyramid is one third the product of its height and the area of its base. The height of the pyramid is , so the volume is

The volume of the cube is , so

,

or, equivalently,

That is, the volume of the cube is six times that of the pyramid, and, since the pyramid has volume 100, the volume of the cube is .

Since the radius is 4, the area of the base is .  To cancel out the , the height must be .

If the diameter of the cylinder is 4, the radius is equal to 2. Therefore:

The answer is .  To find the surface area we need to find the area of the top, bottom, and the round side respectively.  To find the areas of the top and bottom circles, you would need to use the formula  . 

Plug in 4 for , and you get , then multiply by 2 for 2 circles to get 

Then to get the area of the round side, you would take the circumference times the height.  Thus with the formula

you would get  

To get your final answer, add  and  to get   

Also you could remember the formula 

 and plug in  and . 

The surface area of the whole cylinder = (2 * area of circle) + lateral area

Think of the lateral area as the paper label on a can; It wraps around the outside of the can while leaving the top and bottom untouched. The area of the circle, times 2, is to account for the top and the bottom of the cylinder.

Area of a circle =

So the area of the circle = , and since there are two circles we have

Now for the lateral area. Notice how if we have a can with a paper label, we can take the label, cut it, and unroll it from the can. In this way, our label now looks like a rectangle with a

height = height and the

width = circumference of the circle.

Circumference =

So our rectangle is going to have a height of 10 and a width of 10. So the lateral area =

So the total surface area =

The formula to find the surface area of a cylinder is , where  is the height of the cylinder and  is the radius. 

In this kind of equation-based problem, it's helpful to ask "What information do I have?" and "What information is missing that I need?" 

The problem provides information for the  component of the equation, but not for the  component. Instead, we're given information about the circumference of the circular base of the cylinder. The question that arises now is how the radius can be calculated from the circumference. The formula for circumference is: , where  is diameter. Radius can be calculated by taking half of the diameter. This means that radius and circumference are related in terms of . 

Therefore, the first step for this problem is to solve for .

Because the diameter is , that means that the radius must be .

Now the surface area can be solved for after the  and  values are substituted into the equation. 

To find the surface area of the cylinder, first find the areas of the bases:

Next, find the lateral surface area, which is a rectangle:

Add the two together to get the equation to find the surface area of a cylinder:

Plug in the given height and radius to find the surface area.

Make sure to round to  places after the decimal point.

To find the surface area of the cylinder, first find the areas of the bases:

Next, find the lateral surface area, which is a rectangle:

Add the two together to get the equation to find the surface area of a cylinder:

Plug in the given height and radius to find the surface area.

Make sure to round to  places after the decimal point.

To find the surface area of the cylinder, first find the areas of the bases:

Next, find the lateral surface area, which is a rectangle:

Add the two together to get the equation to find the surface area of a cylinder:

Plug in the given height and radius to find the surface area.

Make sure to round to  places after the decimal point.