Answer:
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.
