Question

what is the volume of a cylinder, in cubic centimeters, with a height of 8 centimeters and a base diameter of 4 centimeters? round to the nearest tenths place.

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Find the radius from the diameter

Given the diameter \( d = 4 \) cm, the radius \( r=\frac{d}{2}=\frac{4}{2} = 2 \) cm.

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know \( r = 2 \) cm and \( h=8 \) cm. Substituting into the formula \( V=\pi r^{2}h \), we get \( V=\pi\times(2)^{2}\times8 \).

Step4: Calculate the volume

First, calculate \( (2)^{2}=4 \). Then, \( 4\times8 = 32 \). So \( V = 32\pi \). Using \( \pi\approx3.14159 \), we have \( V\approx32\times3.14159=100.53088 \) cubic centimeters.

Step5: Round to the nearest tenths place

Rounding \( 100.53088 \) to the nearest tenths place, we look at the hundredths digit which is 3. Since \( 3<5 \), we keep the tenths digit as it is. So \( V\approx100.5 \) cubic centimeters.

Answer:

\( 100.5 \) cubic centimeters