Question

what is the volume of a cylinder, in cubic centimeters, with a height of 12 centimeters and a base diameter of 14 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 that the diameter \( d = 14 \) cm, the radius \( r=\frac{d}{2}=\frac{14}{2} = 7 \) cm.

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

We know that \( r = 7 \) cm and \( h=12 \) cm. Substituting these values into the formula \( V=\pi r^{2}h \), we get \( V=\pi\times(7)^{2}\times12 \).
First, calculate \( 7^{2}=49 \). Then, \( V=\pi\times49\times12=588\pi \).

Step4: Calculate the numerical value and round to the nearest tenths place

Using the approximation \( \pi\approx3.14159 \), we have \( V = 588\times3.14159\approx1847.2592 \). Rounding to the nearest tenths place (one decimal place), we look at the hundredths digit, which is 5. Since 5 is greater than or equal to 5, we round up the tenths digit. So, \( 1847.2592\approx1847.3 \).

Answer:

The volume of the cylinder is approximately \( 1847.3 \) cubic centimeters.