When asked to work out the lengths of its edges and its surface area.
Find the area of the base
you don't. you have your teacher do that for you
Yes. A cube's side lengths are all the same, so you really only need one length (l x w x h)
Cube root its volume
We know that the solid is a cube, so all we have to do is find the cubic root of 27 (3). So a cube of volume 27 has dimensions of 3.
The formula for volume is side cubed, and the formula for a square's area is side squared, so you find the cube root of the volume and square your answer to find area.
volume of a cube is length, by width by height. To calculate the volume of a cylinder you need to know the radius and the height and multiply.
If you know the length of one edge simply cube that length. For example, a 3-inch cube = 3 cubed (27) so the volume is 27 cubic inches.
To determine empty space, we will assume that the sphere fits snugly(so that each side of the cube is touching the sphere). First, we take the volume of the cube, which is just one of its side lengths cubed(side length X side length X side length). Record this quantity. Then we find the volume of the sphere. The formula for the volume of a shere is (4/3) Pi r cubed. Since the sphere fits snugly, we know that the radius is half of the side length. We then take the cube volume and subtract the sphere volume, and that is the empty space remaining.
The answer depends on what information you have about the cube. If, for example, you know the volume, V, then the surface area is 6*cuberoot(V)^2. If you have the lengths of an edge, s, then it is 6*s^2.
-- If you don't know anything about the cube, then you just have to measure it. -- If you're told something about the cube, like for example its volume, or the area of a face, or the total area of all its faces, then you can use the formulas you know that express the relationship between the volume or area of a cube and the length of its edges.