A cube is resting on a flat surface. The cube exerts a downward force of 92 newtons on the surface. The pressure on the surface is 23 newtons per metre squared. Calculate the side length of the cube.
𝑃 is equal to 𝐹 over 𝐴, where 𝑃 is pressure, 𝐹 is force, and 𝐴 is area. To calculate pressure, you need to know the force as shown. But you also need to know the surface area over which the force is spread.
We are given that the force is 92 newtons and the pressure is 23 newtons per metre squared. We can therefore substitute this into the formula for pressure to help us calculate the surface area over which the force is spread. That gives us 23 is equal to 92 over 𝐴. To solve this for 𝐴, we first need to multiply both sides of our equation by 𝐴. That gives us 23𝐴 is equal to 92.
Next, we will divide both sides of our equation by 23, giving us that 𝐴 is equal to 92 over 23. We can write out the first four numbers of the 23 times tables to spot that 92 divided by 23 is four. The surface area over which the force is spread is then four metres squared.
However, the question asked us to find the side length of the cube. We know that each face on a cube is a square. We calculated that the area of this square should be four metres squared. Let’s call the dimensions of our square 𝑥. And since the area of a square is found by multiplying its base by its height, we get 𝑥 multiplied by 𝑥, or 𝑥 squared, is equal to four. To solve this equation, we can find the square root of both sides. And the square root of four is just two. This means then that the side length of our cube must be two metres.