The volume of a prism is length times width times height.

We are given the length is 7m and the width is 5m.

So, we plug these into our formula:

 .

We then solve for height:

 .

The height is therefore 6m. 

The goal is to find the height of the rectangular prism with the given information of its width and length. The volume of a rectangular prism is , where  is width and  is height. 

Because we're given the final volume and two of the three variables, we can substitute in the information we know and solve for the missing variable. 

Therefore, the height of the prism is .

If we let  be the width of our prism, then since the length is twice the width, our length would be .  Since the height is twice the length, our height would be .

Since the volume of a rectangular prism is simply the product of width, length, and height, we get

We then simply solve for the width.

Therefore, our width is 3.  Since our length is twice the width, the length is 6.

The formula for the volume of a right, rectangular prism is , so substitute the known values and solve for lenght.  

.  So the length is 8 inches.

Use the formula for finding the surface area of a right, rectangular prism,

and substitute the known values, and then solve for w.

So, 

So, the width is 7 cm.

Since the length of the box is twice the width and the height is three times the width,  and . 

The surface area of the box is

To find the width:

To find the surface area of a prism, the problem can be approached in one of two ways.

1. Through an equation that uses lateral area
2. Through finding the area of each side and taking the sum of all the faces

Using the second method, it's helpful to realize rectangular prisms contain  faces. With that, it's helpful to understand that there are  pairs of sides. That is, there are two faces with the same dimensions. Therefore, we really only have three sides for which we need to calculate areas: 

Faces 1 & 2:

Faces 3 & 4:

Faces 5 & 6:

Now, we can add up the areas of all six sides:

The surface area is .

Since the ramp forms a 45-45-90 triangle, the base of the ramp is equal to the height. So the area of the triangle is  meters. The area of the two triangles would be  meters. The other sides of the ramp are rectangles. Two of the rectangles are the same with one having a different length due to the hypotenuse of the triangle. The two that are the same have a length of 3 and a width of 8. The area for each of these is  meters. Since there are 2 of these, we mulitply 24 by 2. For the last triangle, we must find the hypotenuse of the triangle. Since it is a 45-45-90, the hypotenuse is the base multiplied by . Therefore the last rectangle's is  meters. The find the surface area, all of the areas must be added together. Triangles+rectangles= meters. To the nearest whole meter, the answer is 91 meters.

Since the box has an open top, the surface area is calculated by finding the four sides plus the floor of the box.

The short sides' areas are calculated by multiplying height times width times two, for the two sides: .

The longer sides' areas are calculated by multiplying height times length times two, for the two sides: .

Now, we calculate the area of the floor of the box by multiplying length times width times one, for the only floor and no top: .

Lastly, we add the areas together to calculate the total surface area of the open-top box: ,

Surface area means the entire area that all the sides of a prism take up. 

The surface area can be calculated in one of two ways. One way involves using an equation for lateral area. The other method involves taking the area of all the sides and summing the areas. 

Using the latter of the two methods:

It's helpful to understand that rectangular prisms have three pairs of sides with the same dimensions, making up the total of six faces. This means that only three novel calculations for individual areas of faces need to be calculated. 

Faces 1 & 2:

Faces 3 & 4:

Faces 5 & 6: