Question

a cylinder has a radius of 5.5 centimeters and a height of 6 centimeters. use the pi key on the calculator to find the volume to the nearest tenth of a cubic centimeter. v ≈ \square cm³

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 and \( h \) is the height.

Step2: Substitute the given values into the formula

We are given that \( r = 5.5\) cm and \( h=6\) cm. Substituting these values into the formula, we get \( V=\pi\times(5.5)^{2}\times6 \).
First, calculate \( (5.5)^{2}=5.5\times5.5 = 30.25 \).
Then, multiply by 6: \( 30.25\times6=181.5 \).
So, \( V=\pi\times181.5 \).

Step3: Calculate the volume using the pi key

Using the pi key on the calculator, we have \( V\approx3.141592654\times181.5 \).
Calculating this, \( 3.141592654\times181.5 = 3.141592654\times(180 + 1.5)=3.141592654\times180+3.141592654\times1.5 \)
\( 3.141592654\times180 = 565.4866777 \) and \( 3.141592654\times1.5 = 4.712388981 \)
Adding these together: \( 565.4866777+4.712388981 = 570.1990667 \)
Rounding to the nearest tenth, we look at the hundredth place. The number is \( 570.1990667 \), the hundredth digit is 9, which is greater than 5, so we round up the tenth place. So \( 570.2 \).

Answer:

\( 570.2 \)