Question

the given figure is a cylinder. the radius of the cylinder is 14.9 millimeters and the height of the cylinder is 33.3 millimeters. what is the volume of the cylinder? use the given information to complete the worksheet. use 3.14 as an approximation for π. ab (radius of base) millimeters area of ⊙a square millimeters bc (height of cylinder) millimeters volume of the cylinder cubic millimeters

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume \( V \) of a cylinder is given by the formula \( V=\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cylinder. We are given that \( r = 14.9\) millimeters, \( h=33.3\) millimeters, and \( \pi\approx3.14 \).

Step2: Calculate \( r^{2} \)

First, we calculate \( r^{2}=(14.9)^{2} \).
\( 14.9\times14.9 = 222.01 \)

Step3: Calculate \( \pi r^{2} \)

Now, we multiply \( \pi\) (approximated as 3.14) with \( r^{2} \).
\( 3.14\times222.01=3.14\times222 + 3.14\times0.01=697.08+0.0314 = 697.1114 \) (square millimeters, this is the area of the base)

Step4: Calculate the volume \( V=\pi r^{2}h \)

Now, we multiply the area of the base (\( \pi r^{2} \)) with the height \( h \).
\( V = 697.1114\times33.3 \)
First, calculate \( 697.1114\times30 = 20913.342 \)
\( 697.1114\times3=2091.3342 \)
\( 697.1114\times0.3 = 209.13342 \)
Now, add them together: \( 20913.342+2091.3342 + 209.13342=20913.342+2299.46762=23212.80962 \)

Answer:

The volume of the cylinder is approximately \( 23212.81 \) cubic millimeters.