Given data:
circumference of a cylinder = 3 3/4
volume of the cylinder = 7.
to find the height of the cylinder.
Use the formula,
[tex]v=\pi\cdot(\frac{c}{2\pi})^2\cdot h[/tex]
subsitute the values in the formula,
[tex]\begin{gathered} 7=\pi\cdot(\frac{\frac{15}{4}}{2\pi})^2\cdot h \\ 7=\frac{22}{7}\cdot(\frac{\frac{15}{4}}{2\cdot\frac{22}{7}})^2\cdot h \\ 7=\frac{22}{7}\cdot(\frac{15}{8\cdot\frac{22}{7}})^2\cdot h \\ \frac{22\cdot\:15^2}{7\cdot\:8^2\cdot\frac{22^2}{7^2}}\cdot h=7 \\ \frac{15^2\cdot\:22}{\frac{30976}{7}}\cdot h=7 \\ \frac{22\cdot\:15^2\cdot\:7}{30976}\cdot h=7 \\ \frac{15^2\cdot\:7}{1408}\cdot h=7 \\ \frac{1575}{1408}\cdot h=7 \\ 1575h=9856 \\ h=\frac{1408}{225} \\ h=6.25 \end{gathered}[/tex]
The height of the cylinder is 6.3 in.
