Question

the volume of this cylinder is 1,846.32 cubic millimeters. what is the radius? round your answer to the nearest hundredth. 12 mm r ≈ millimeters

Explanation:

Step1: Write the formula for the volume of a cylinder

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

Step2: Substitute the given values into the formula

Given \( V = 1846.32\) cubic millimeters and \( h=12\) millimeters. So, \( 1846.32=\pi r^{2}\times12\).

Step3: Solve for \( r^{2} \)

First, divide both sides by \( 12\pi \). \( r^{2}=\frac{1846.32}{12\pi}\). Taking \( \pi = 3.14\), we have \( r^{2}=\frac{1846.32}{12\times3.14}=\frac{1846.32}{37.68} = 49\).

Step4: Solve for \( r \)

Since \( r^{2}=49\), then \( r=\sqrt{49}= 7.00\) (because radius cannot be negative).

Answer:

\(7.00\)