Question

A cylinder with a height of 6 1/2 inches. (In) and a diameter of 5 inches is shown.

Answer 1

Answer:

$\large\boxed{V\approx127.5625\ in^3}$

Step-by-step explanation:

The formula of a volume of a cylinder:

$V=\pi r^2H$

r - radius

H - height

We have:

$2r=5\ in\to r=2\dfrac{1}{2}\ in\\\\H=6\dfrac{1}{2}\ in$

Convert the mixed numbers to the impropoer fractions:

$2\dfrac{1}{2}=\dfrac{2\cdot2+1}{2}=\dfrac{5}{2}\\\\6\dfrac{1}{2}=\dfrac{6\cdot2+1}{2}=\dfrac{13}{2}$

Substitute:

$V=\pi\left(\dfrac{5}{2}\right)^2\left(\dfrac{13}{2}\right)=\pi\left(\dfrac{25}{4}\right)\left(\dfrac{13}{2}\right)=\dfrac{325}{8}\pi\ in^3\\\\\pi\approx3.14\\\\V\approx\dfrac{325}{8}\cdot3.14=40.625\cdot3.14=127.5625\ in^3$