a cylinder has a base radius of 7 centimeters and a height of 6 centimeters. what is its volume in cubic…

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: Substitute the given values into the formula

We are given that ( r = 7 ) centimeters and ( h=6 ) centimeters. Substituting these values into the formula, we get ( V=\pi\times(7)^{2}\times6 ). First, calculate ( 7^{2}=49 ). Then the expression becomes ( V = \pi\times49\times6 ). Calculate ( 49\times6 = 294 ), so ( V=294\pi ).

Step3: Calculate the numerical value

Using the approximation ( \pi\approx3.14159 ), we have ( V\approx294\times3.14159 ). ( 294\times3.14159 = 294\times3+294\times0.14159=882 + 294\times0.14159 ). ( 294\times0.14159\approx294\times0.14 = 41.16 ) and ( 294\times0.00159\approx0.467 ), so ( 294\times0.14159\approx41.16 + 0.467 = 41.627 ). Then ( 882+41.627 = 923.627 ).

Step4: Round to the nearest tenths place

The number ( 923.627 ) rounded to the nearest tenths place is ( 923.6 ) (since the hundredths digit is 2, which is less than 5, we leave the tenths digit as it is).

Answer:

( 923.6 )