Question

The volume of cube is 343 cubic centimeters. what is the surface area of the cube? show your work.

Answer 1

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!