Given the formula for volume:
[tex]V\text{ = }\pi r^2h[/tex]Let's rewrite the formula in terms r, V and h.
i) Rewriting for r in terms of V and h :
[tex]\begin{gathered} V\text{ = }\pi r^2h \\ \frac{V}{h}=\pi r^2 \\ \\ \sqrt[]{\frac{V}{\pi h}}=r \\ \\ r\text{ = }\sqrt[]{\frac{V}{\pi h}} \end{gathered}[/tex]2) Given:
Volume, V = 66 cubic inches
height, h = 3.3 inches
We know that diameter is radius multiplied by 2.
To find the diameter, first find the radius.
Therefore, we have:
[tex]\begin{gathered} r\text{ = }\sqrt[]{\frac{V}{\pi h}} \\ \\ r\text{ = }\sqrt[]{\frac{66}{3.3\pi}} \\ \\ r\text{ = }2.52\text{ inches} \end{gathered}[/tex]Since the radius is 2.52 inches, the dia,eter will be:
D = r x 2 = 2.52 x 2 = 5.04 inches
To the nearest inch = 5 inches
ANSWER:
diameter = 5 inches
