# A circular piston exerts a pressure of 80 k Pa on a fluid, when the force applied to the piston is 0.2kN. What is the diameter of the piston ?

Oct 1, 2017

$P = \frac{F}{A}$ rearranged for area, A. You then need to find the diameter from $A = \pi {r}^{2}$ remembering to double the radius to get diameter.

#### Explanation:

A = $\frac{F}{P} = \frac{200}{80000}$

A = $0.0025 {m}^{2}$

r = $\sqrt{\frac{A}{\pi}}$ = sqrt(0.0025/pi

r = 0.028 $m$

D = 2r = 0.056 m

Oct 1, 2017

The diameter is 0.056 m.

#### Explanation:

Pressure is force divided by area.
Therefore, by the manipulations of algebra, area = force/pressure.

So the area of the piston is given by
$\text{area} = \frac{0.2 k N}{80 k P a} = \frac{0.2 \cdot \cancel{{10}^{3}} \cancel{N}}{80 \cdot \cancel{{10}^{3}} \frac{\cancel{N}}{m} ^ 2} = 0.0025 {m}^{2}$

To find diameter we first need to get the radius using the formula for the area of a circle.
area = $\pi \cdot {r}^{2} \to$ from that, we can obtain
$r = \sqrt{\frac{\text{area}}{\pi}} = \sqrt{\frac{0.0025 {m}^{2}}{\pi}} = 0.028 m$

So the diameter is 0.056 m.

Or 5.6 cm if you prefer.

I hope this helps,
Steve