Answer:
[tex]625\ \text{cm}^2[/tex]
[tex]14.1\ \text{cm}[/tex]
Explanation:
[tex]F_1[/tex] = Force applied to master piston = 200 N
[tex]F_2[/tex] = Force applied to slave piston = 5000 N
[tex]A_1[/tex] = Area of master piston = [tex]25\ \text{cm}^2[/tex]
[tex]A_2[/tex] = Area of slave piston
r = Radius of slave piston
From Pascal's law we have
[tex]\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2}\\\Rightarrow A_2=\dfrac{F_2}{F_1}A_1\\\Rightarrow A_2=\dfrac{5000}{200}\times 25\\\Rightarrow A_2=625\ \text{cm}^2[/tex]
The area of the slave piston is [tex]625\ \text{cm}^2[/tex]
Area of the slave piston is given by
[tex]A_2=\pi r^2\\\Rightarrow r=\sqrt{\dfrac{A_2}{\pi}}\\\Rightarrow r=\sqrt{\dfrac{625}{\pi}}\\\Rightarrow r=14.1\ \text{cm}[/tex]
The radius of the slave piston is [tex]14.1\ \text{cm}[/tex].
