Question

determine the volume of the shaded region. use the π button on your calculator. the volume of the shaded region is . (simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)

Explanation:

Step1: Find volume of outer - cylinder

The formula for the volume of a cylinder is $V = \pi r^{2}h$. The radius of the outer - cylinder $r_{1}=\frac{2}{2}=1$ cm and height $h = 5.6$ cm. So, $V_{1}=\pi\times(1)^{2}\times5.6 = 5.6\pi$ $cm^{3}$.

Step2: Find volume of inner - cylinder

The radius of the inner - cylinder $r_{2}=\frac{1.8}{2}=0.9$ cm and height $h = 5.6$ cm. So, $V_{2}=\pi\times(0.9)^{2}\times5.6=\pi\times0.81\times5.6 = 4.536\pi$ $cm^{3}$.

Step3: Find volume of the shaded region

The volume of the shaded region $V = V_{1}-V_{2}$. Substitute the values of $V_{1}$ and $V_{2}$: $V=(5.6\pi - 4.536\pi)=1.064\pi$ $cm^{3}$. Using $\pi$ from the calculator, $V = 1.064\times3.14159\approx3.33$ $cm^{3}$.

Answer:

$3.33$