Question

anand models a can of ground coffee as a right cylinder. he measures its radius as \\( \frac { 1 } { 2 } \\) in and its volume as 4 cubic inches. find the height of the can in inches. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Write the formula for the volume of a cylinder

The volume \( V \) of a right - 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 know that \( V = 4\) cubic inches and \( r=\frac{1}{2}\) inch. Substituting these values into the formula \( V=\pi r^{2}h\), we get \( 4=\pi(\frac{1}{2})^{2}h\).

First, calculate \( (\frac{1}{2})^{2}=\frac{1}{4}\). So the equation becomes \( 4=\frac{\pi}{4}h\).

Step3: Solve for \( h \)

To solve for \( h \), we can multiply both sides of the equation \( 4=\frac{\pi}{4}h\) by \(\frac{4}{\pi}\).

$$ h=\frac{4\times4}{\pi}=\frac{16}{\pi} $$

Since \(\pi\approx3.14\), then \( h=\frac{16}{3.14}\approx5.1\)

Answer:

\(5.1\)