Question

what is the volume, in cubic centimeters, of a cylinder with a height of 9 centimeters and a base radius of 7 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 \(r = 7\) cm and \(h=9\) cm. Substitute these values into the formula: \(V=\pi\times(7)^{2}\times9\).
First, calculate \((7)^{2}=49\). Then \(V=\pi\times49\times9\).
\(49\times9 = 441\), so \(V = 441\pi\).

Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(V=441\times3.14159\).
\(441\times3.14159=(400 + 40+1)\times3.14159=400\times3.14159+40\times3.14159 + 1\times3.14159\)
\(400\times3.14159 = 1256.636\), \(40\times3.14159=125.6636\), \(1\times3.14159 = 3.14159\)
\(V=1256.636+125.6636 + 3.14159=1385.44119\)

Step4: Round to the nearest tenths place

To round \(1385.44119\) to the nearest tenths place, look at the hundredths digit. The hundredths digit is \(4\). Since \(4\lt5\), we keep the tenths digit as it is.

Answer:

\(1385.4\) cubic centimeters