Question

given the cylinder with diameter of 12 in and height of 6 in. what is the approximated volume, in cubic inches, of the cylinder? round the answer to the nearest cubic inch (no decimals).

Explanation:

Step1: Find the radius

The radius $r$ of a circle is half of the diameter. Given diameter $d = 12$ in, so $r=\frac{d}{2}=\frac{12}{2}=6$ in.

Step2: Use the volume formula for a cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$. Substitute $r = 6$ in and $h=6$ in into the formula: $V=\pi\times6^{2}\times6=\pi\times36\times 6 = 216\pi$ in³.

Step3: Approximate the value

Take $\pi\approx3.14$, then $V\approx216\times3.14 = 678.24$ in³. Rounding to the nearest cubic - inch, $V\approx678$ in³.

Answer:

678