Pressure Force Area

 

 

We are calculating the pressure, so  by covering up p, we can see from the triangle above that we have to divide F by A.

Before we can do this calculation however, we need to work out the area of the square.  Since the square has  a side length of 3 m, the area can be calculated as follows:

3 m \times \, 3 m = 9 m^2

 

Now that we have the area and the force, we can calculate the pressure by substituting the values for the area and the force into the pressure equation as follows:

\text{pressure }=\dfrac{F}{A}=\dfrac{185.6}{9}=20.6222...=20.6 N/m^2 (3 sf).

 

The units must be N/m^2 since the units used in the question are N and m^2.

 

 

We are calculating the area, so by covering up A, we can see from the triangle above that we have to divide F by p.  So, by substituting the known values for the force and the pressure into the equation, we can calculate the area as follows:

\text{Area }=\dfrac{F}{p}=\dfrac{740}{2312.5}=0.32latex] m[latex]^2

 

The unit must be m^2 since the units used in the question are N/m^2.

In this question, we are calculating the force, so we will need to rearrange the pressure / force  / area equation.

Since

\text{pressure = force} \div \text{ area}

then

\text{force = pressure} \times \text{ area}

 

By substituting the values for the pressure and the area into the formula above, we can calculate the force as follows:

\text{Force } = 16 m^2 \times \, 2480 N/m^2 = 39,680 N

This may seem like an impossible question without sufficient information to go by at first glance.  We have been given the pressure as well as the weight (force) of the cylinder.  Since we know both the force and the pressure, the only thing we are able to calculate at this stage is the area of the circular cylinder face.

 

Since

\text{pressure = force} \div \text{ area}

then

\text{area = force} \div \text{ pressure}

 

By substituting the values for the force and the pressure into the formula above, we can calculate the area as follows:

4872 N \div \, 812 N/m^2 = 6 m^2

 

We now know that the area of the circular face on which the cylinder is resting has an area of 6 m^2, and from this information we need to work out the diameter of the cylinder / circle.  In this question, we therefore need to apply some basic knowledge about the circle areas.

The formula for the area of a circle is \pi r².

However, we know the area and want a formula for the radius, so we will need to rearrange this formula.

First of all, we can both sides by \pi:

\dfrac{a}{π} = r^2

If we now take the square root of both sides, we have a formula for the radius:

\sqrt \dfrac{a}{π} = r

 

Since we know the area, all we need to do is divide the area by \pi, and square root the answer.

6 \div \pi = 1.9099

\sqrt {1.9099} = 1.38 m

If the radius of the circle is 1.38m, then the diameter will be double this:

\text{Diameter} = 2 \times 1.38 = 2.76 m

This is another of these questions that might seem impossible initially, but there is sufficient information in the question to solve it.  Like many maths problems, if you don’t have a clear strategy, just do any calculations you can, as they may lead somewhere useful!