The volume of the cylinder is 170cm³ and the height is 9cm. Work out the diameter.

The diameter of the cylindeer is 4.91 cm.

Step-by-step explanation:

The formula for the volume of a cylinder of radius r and height h is

V = πr²h.  Recall that 2r = d and that r = d/2, so that r² =d²/4.  Now solve V = πr²h for r² and then substitute d²/4 for r²:

           V              d²

r² = =      Multiplying all three terms of this equation by 4

         πh               4           yields an equation for d²:

         4V              

      =       d²    

         πh              

Now substitute 170 cm³ for V and 9 cm for h.  then we have an expression

for d²:

4(170 cm³)        680 cm²

= = d² = 24.06 cm²

  π(9 cm)            9(3.14)

Finally, take the square root of both sides to obtain an expression for d:

d = +√(24.06 cm²) = 4.91 cm

The diameter of the cylindeer is 4.91 cm.