Question

a given circular cylinder has a radius of 5 inches (in) and a height of 10 in. calculate the volume of the cylinder using \\(\frac{22}{7}\\) for \\(pi\\) and round to the nearest thousandth.

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume \( V \) of a circular cylinder is given by the formula \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute the given values into the formula

We are given that \( r = 5\) inches, \( h=10\) inches and \( \pi=\frac{22}{7} \). Substituting these values into the formula, we get:
\( V=\frac{22}{7}\times(5)^{2}\times10 \)

Step3: Calculate \( (5)^{2} \)

\( (5)^{2}=25 \), so the expression becomes \( V = \frac{22}{7}\times25\times10 \)

Step4: Multiply the numbers

First, multiply \( 22\times25\times10 \): \( 22\times25 = 550 \), and \( 550\times10=5500 \). Then divide by 7: \( V=\frac{5500}{7}\approx785.714 \) (rounded to the nearest thousandth)

Answer:

\( 785.714 \) cubic inches (or \( 785.714\space in^{3} \))