hello
to solve this problem, let's write down the data given
Area = 250cm^2
radius = 4cm
height = ?
surface area (A) =
[tex]\begin{gathered} A=2\pi rh+2\pi r^2 \\ \pi=\frac{22}{7}=3.14 \end{gathered}[/tex]now, let's substitute the values into the equation
[tex]\begin{gathered} A=2\pi rh+2\pi r^2 \\ 250=2\times3.14\times4\times h+2\times3.14\times4^2 \\ 250=25.12h+100.48 \\ \text{solve for h} \\ 250-100.48=25.12h \\ 149.52=25.12h \\ \text{divide both sides by 25.12} \\ \frac{149.52}{25.12}=\frac{25.12h}{25.12} \\ h=5.95\operatorname{cm} \end{gathered}[/tex]the height of the cylinder is equal to 5.95cm
