Step-by-step explanation:
It is given that, when a box rests on a round sheet of wood on the ground, it exerts an average pressure p on the wood. Let A is the area of box having radius r.
Pressure is given by,
![P=(F)/(A)](https://img.qammunity.org/2020/formulas/physics/college/w6dmjhgoa2nqzut32hmrr8jf5dlyl9vj0l.png)
![P\propto (1)/(A)](https://img.qammunity.org/2020/formulas/physics/college/l9bxakdgq5afqbpslslg0qsbodrhmz69ki.png)
![A=\pi r^2=\pi (d/2)^2](https://img.qammunity.org/2020/formulas/physics/college/vbxzwp2ewwgz0jsvvkypbk8jwu31bhl152.png)
![P_1=(4F)/(\pi d_1^2)](https://img.qammunity.org/2020/formulas/physics/college/d53dm8730fvnblvzp1gpws8av0kymrqb0r.png)
If the wood is replaced by a sheet that has half the diameter of the original piece,
![P=(4F)/(\pi d_2^2)](https://img.qammunity.org/2020/formulas/physics/college/ml3l6q41swnzc57aczovjionc80836rxn6.png)
![d_2=(d_1)/(2)](https://img.qammunity.org/2020/formulas/physics/college/3n14yo643io8hgi7lnwp8vxwuc2ifyjfne.png)
![P_2=4* (4F)/(\pi d_1^2)](https://img.qammunity.org/2020/formulas/physics/college/zspbvbh8tc8qquzyaf1cdxdq69bd2ivygs.png)
![P_2=4* P_1](https://img.qammunity.org/2020/formulas/physics/college/5hpnilbkbj73altlpan8nfg1x2934grh5h.png)
So, new pressure is four times of the initial pressure. Hence, this is the required solution.