If the edge of the cube is reduced by 5, then the surface area is reduced by 450. Find the volume of the cube.

We do not know the length of the edge of the cube, so we should designate it as x cm, then we write down what the length of the edge will equal after decreasing – (x – 5) cm, then we write down what the difference between the initial surface area of the cube and the final one will be:

6 * x ^ 2 – 6 * (x – 5) ^ 2 = 450.

Let’s open the square:

6 * x ^ 2 – 6 * (x ^ 2 – 10x + 25) = 450.

Let’s open the brackets, we will reduce similar terms:

60x = 600;

x = 10 cm.

We found that the length of the edge was initially 10 cm, we find the volume of the cube:

V = 10 ^ 3 = 1000 cm3.

Answer: 1000 cm3