Statement 1: The information provided in the question is only useful if we're given a relationship between cube A and cube B. Since this statement does provide us with the ratio of 1:2, we can answer the question.

where  represents the length of the cube's edge

we can easily see the length measures 

Remember the ratio of cube A to cube B is 1:2.

Now that we know the length, we can find the diagonal of the cube:

Statement 2: We're given information about cube A so we don't need to worry about cube B. Using this information we can solve for the edge length of cube A and then calculate the diagonal.

Knowing the length of the edge allows us to find the diagonal of the cube

To find the surface area of a cube, we need the length of one side. 

Statement I gives the diagonal, we can use this to find the length of one side.

Statement II gives us a clue about the length of one side; we can use that to find the full length of one side.

The following formula gives us the surface area of a cube:

Use Statement I to find the length of the side with the following formula, where  is the diagonal and  is the side length:

So, using Statement I, we find the surface area to be

Using Statement, we get that the length of one side is two times two:

Again, use the surface area formula to get the following:

To find the volume of a cube, we only need the length of one side. Using statement 1, we can figure out the length of a side based on the diagonal. We can use the figure below to find the ratio of the diagonal to one side. If the we let the length of one side be x, we can use Pythagorean's theorem to find the length of the diagonal. So, in triangle BCD, we have a right triangle, with two sides of length x. We can set up the equation that the length of BD is .

Then we can see triangle ADB is also a right triangle. Using Pythagorean's theorem we get the length of AB is .

So, if we divide the number from statement 1 by the square root of 3, we get the length of each side of the cube. Doing this, we get . Thus, we can solve this problem with just the information from statement 1. 

Now, we can also check statement 2. If we know the surface area of the cube, we can use that information to find the length of each side of the cube. We know that the surface area of a cube is the sum of the six faces of the cube, which all have equal area and are all squares. We can divide the total surface area by 6 to find the surface area of each square face. So, 600/6 = 100. We know that the area of a square is just the length of one side squared, so we can take the square root of 100 to find that the length of each side is 10. Thus statement 2 is also sufficient to solve this problem.

Therefore, the answer is that either statement alone is sufficient to answer the question.  

The weight of a cube is dependent on its density in pounds per cubic foot and its volume in cubic feet. We need Statement 1 for the density. Statement 2 is needed for the volume - and it gives us the means to find it, since we can take the square root of the area of one side, 16, to get sidelength 4 feet, and we can cube that to get the volume of 64 cubic feet. Now we can multiply 64 cubic feet by 3 pounds per cubic foot to get 192 pounds.

If we know the base of W, we can find the side length. We then cube the side length to find the volume of a square. 

If we know the diagonal of the base of W, we can find the side length. As outlined above, we can then cube the side length to find the volume.

Therefore either statement alone is sufficient to solve the question.

Statement 1: We need the length of the edge of the cube to calculate the volume. In this statement we're provided with the length so we just need to plug it into the equation for a cube's volume.

Statement 2: In this case, we need to solve for the length of the cube's edge which we can easily do: 

Now that we have our length, we can calculate the volume.

Recall that the volume of a cube is equal to the cube of its side length, and that the diagonal of a cube is equal to  length. 

I) Use the following:

II) Gives us the diagonal. Divide by the square root of three, then cube it!

Either statement is sufficient to answer the question.

To know the volume of the box, which is shaped like a rectangular prism, you multiply the length, the width, and the height together. Neither statement alone gives you those dimensions, just clues as to how they are related. But together, you can form a system of linear equations using height  and width (and length) .

By the first and second statements, respectively, 

This system can be solved:

From this, you can determine the length and height, and, subsequently, the volume.

To find surface area, we need to know the side length of the box.

We are told the box has equal length, width and height. This means it is a cube.

I) Gives us the diagonal of the cube, from this we can find the side length.

, where s is the side length.

Now we can use the side length to find the surface area of the box.

II) Gives us the volume of the cube, from which we can also find the side length.

From here we can find the surface area.

Thus, either statement is sufficient.

Fry recently met a robot known for bending things. The robot wants to make a box out of steel by bending a single sheet of metal. Find the total area of the sheet of metal given the following:

I) The box will be  long

II) The box's height will be 2 feet taller than its length, and the box's width will be  less than its length.

This question is a surface area question in disguise. To find the surface area of a prism, we need the area of each side. Begin by using I and II to find each side length:

Length: 36 inches or 3 feet

Height:  or 5 feet

Width:  or 

So, we have all our side lengths. Next, use the following formula for surface area of a rectangular prism:

Where l,w, and h are length, width and height