When a box rests on a round sheet of wood on the ground, it exerts an average pressure p on the wood. if the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure? i think the answer is 4p but i don't know why.

Pressure = Force ÷ Area

In this case, since the area is circular, we can rewrite the equation as:

Pressure = Force ÷ pi*r^2

Decreasing the diameter by half is the same as decreasing the radius by half.

We can replace all constants with 1 to compare the relationship between the two scenarios.

Original scenario with original area wood:

Pressure = 1 ÷ 1^2
Pressure = 1

Scenario with 0.5 radius of original scenario:
Pressure = 1 ÷ (1/2)^2
Pressure = 1 ÷ 1/4
Pressure = 4

This confirms that your guess of 4x the pressure is correct.

So as can be seen by the relationship, pressure for circular area is inversely proportional to the radius squared.

Your answer is 1.5 hope i