Question

what is the volume of a cylinder, in cubic centimeters, with a height of 9 centimeters and a base diameter of 12 centimeters? round to the nearest tenths place.
answer attempt 1 out of 2
v =
show examples

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.

Step2: Find the radius from the diameter

Given the diameter \( d = 12 \) cm, the radius \( r=\frac{d}{2}=\frac{12}{2} = 6 \) cm.

Step3: Substitute the values into the formula

We know \( r = 6 \) cm and \( h=9 \) cm. Substitute these into the formula: \( V=\pi\times(6)^{2}\times9 \).
First, calculate \( 6^{2}=36 \), then \( 36\times9 = 324 \). So \( V=\pi\times324\approx3.14159\times324 \).

Step4: Calculate the numerical value

\( 3.14159\times324 = 1017.87616 \).

Step5: Round to the nearest tenths place

The tenths place is the first digit after the decimal. The number is \( 1017.87616 \), the digit in the hundredths place is 7, which is greater than 5, so we round up the tenths place. So \( 1017.87616\approx1017.9 \).

Answer:

\( 1017.9 \)