The volume of a rectangular prism is .

We are told that the shortest edge is 3. Let us call this the height.

We now have , or .

Now we replace variables by known values:

Now we have:

We have thus determined that the other two edges of the rectangular prism will be 4 and 12. We now need to find the longest diagonal. This is equal to:

If you do not remember how to find this directly, you can also do it in steps. You first find the diagonal across one of the sides (in the plane), by using the Pythagorean Theorem. For example, we choose the side with edges 3 and 4. This diagonal will be:

We then use a plane with one side given by the diagonal we just found (length 5) and the other given by the distance of the 3rd edge (length 12).

This diagonal is then .

A cube with a side length of 25m has a surface area of:

25m * 25m * 6 = 3,750 m2

(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)

Each square tile has an area of 5 m2.

Therefore, the total number of square tiles needed to fully cover the surface of the cube is:

3,750m2/5m2 = 750

Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:

s3/n3

The volume of a rectangular prism is .

We are told that the shortest edge is 3. Let us call this the height.

We now have , or .

Now we replace variables by known values:

Now we have:

We have thus determined that the other two edges of the rectangular prism will be 4 and 12. We now need to find the longest diagonal. This is equal to:

If you do not remember how to find this directly, you can also do it in steps. You first find the diagonal across one of the sides (in the plane), by using the Pythagorean Theorem. For example, we choose the side with edges 3 and 4. This diagonal will be:

We then use a plane with one side given by the diagonal we just found (length 5) and the other given by the distance of the 3rd edge (length 12).

This diagonal is then .

A cube with a side length of 25m has a surface area of:

25m * 25m * 6 = 3,750 m2

(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)

Each square tile has an area of 5 m2.

Therefore, the total number of square tiles needed to fully cover the surface of the cube is:

3,750m2/5m2 = 750

Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:

s3/n3

The area of a cube is equal to the measure of one edge cubed. If we take the cube root of , we get , so the edges of this cube measure ; therefore, one face of the cube has an area of square inches, because .

There are sides to a cube, so

The area of a cube is equal to the measure of one edge cubed. If we take the cube root of , we get , so the edges of this cube measure ; therefore, one face of the cube has an area of square inches, because .

There are sides to a cube, so

If the surface area is , then the area of one face must be . Therefore, the length of one edge must be This means that the volume of the cube is . We can now solve with:

If the surface area is , then the area of one face must be . Therefore, the length of one edge must be This means that the volume of the cube is . We can now solve with: