Answer:
h = 1.38 cm
Step-by-step explanation:
The question is at what value is the height of both cylinders the same:
The area of the circular base on each cylinder is:
[tex]Area=\pi r^2\\A=4\pi \ cm^2\\B=25\pi \ cm^2[/tex]
The initial volume in cylinder A is:
[tex]V=4\pi *10\\V=40\pi\ cm^3[/tex]
We have that Va + Vb = 40π. The height of water in each cylinder as a function of volume is:
[tex]h_A=\frac{V_a}{4\pi}\\h_B=\frac{V_b}{25\pi}[/tex]
If both heights are the same:
[tex]\frac{V_a}{4\pi}=\frac{V_b}{25\pi}\\V_b=\frac{25}{4}V_a \\V_a+V_b=40\pi\\V_a+\frac{25}{4}V_a=40\pi\\V_a=5.5172\pi\ cm^3[/tex]
The height 'h' is:
[tex]h=\frac{5.5172\pi}{4\pi}\\ h=1.38\ cm[/tex]
