In short, the surface area of the cube is 294cm^2.
To find volume of a cube, a side is multiplied by itself three times. So, we have this so far, let "s" equal a side of the cube... s*s*s or s^3 = volume. But, we have to work backwards to find s. We know the volume is 343 cm^3 and we know to find volume we take a side and multiply it by itself three times, also known as cubing a side.
So, s^3 = 343 cm^3. To find what one s equals, we have to take the cube root of 343. A cube root is the opposite of cubing a side and that's why it works.
Basically, we're trying to find what number times itself three times will equal 343. A cube root of 343 will tell us the answer. So, once we cube root 343, we get 7. This means that 7 is one s or the side length of the cube. Remember, a cube has all equal sides, so 7 is the side lengths for the whole cube.
Now, to find surface area of a cube, the formula is 6*s^2. This means that the side is squared times six. We already know what the side is, 7, and order of operations, PEMDAS, tells us that exponents come before multiplication. So, we have 7^2 which is 49 times 6. 49 * 6 = 294. Hope this helped!
The shape is a cuboid and it has 6 faces, and the opposite faces are equal, so I calculate 3 different faces and multiplied it by 2 to give me the total surface area. Therefore, total surface area = the addition of all the surface areas in the shape. And to get each surface area, you have find the area of each of the 6 faces, and add them together, to give you the total surface area.
