Question

what is the volume, in cubic centimeters, of a cylinder with a height of 15 centimeters and a base radius of 6 centimeters, 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.

Step2: Substitute the given values into the formula

Given \( r = 6\) cm and \( h=15\) cm. Substitute these values into the formula: \( V=\pi\times(6)^{2}\times15\).
First, calculate \( (6)^{2}=36\). Then \( V=\pi\times36\times15\).
\( 36\times15 = 540\), so \( V = 540\pi\).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159\), then \( V=540\times3.14159\).
\( 540\times3.14159=1696.4586\).

Step4: Round to the nearest tenths place

The digit in the hundredths place is \( 5\). Using the rounding rule (if the digit in the hundredths place is \( 5\) or greater, we round up the digit in the tenths place), \( 1696.4586\approx1696.5\).

Answer:

\(1696.5\)