Answer:
[tex]\large\boxed{V\approx127.5625\ in^3}[/tex]
Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have:
[tex]2r=5\ in\to r=2\dfrac{1}{2}\ in\\\\H=6\dfrac{1}{2}\ in[/tex]
Convert the mixed numbers to the impropoer fractions:
[tex]2\dfrac{1}{2}=\dfrac{2\cdot2+1}{2}=\dfrac{5}{2}\\\\6\dfrac{1}{2}=\dfrac{6\cdot2+1}{2}=\dfrac{13}{2}[/tex]
Substitute:
[tex]V=\pi\left(\dfrac{5}{2}\right)^2\left(\dfrac{13}{2}\right)=\pi\left(\dfrac{25}{4}\right)\left(\dfrac{13}{2}\right)=\dfrac{325}{8}\pi\ in^3\\\\\pi\approx3.14\\\\V\approx\dfrac{325}{8}\cdot3.14=40.625\cdot3.14=127.5625\ in^3[/tex]
