find the volume of the figure. express answers in terms of $\\pi$, then round to the nearest whole…

find the volume of the figure. express answers in terms of $\\pi$, then round to the nearest whole number.\n\nexpress the volume of the figure in terms of $\\pi$.\n\n(type an exact answer in terms of $\\pi$.)

find the volume of the figure. express answers in terms of $\\pi$, then round to the nearest whole number.\n\nexpress the volume of the figure in terms of $\\pi$.\n\n(type an exact answer in terms of $\\pi$.)

Answer

Explanation:

Step1: Identify the geometric figure and dimensions

The figure is a cylinder with radius $r = 8\text{ m}$ and height $h = 10\text{ m}$.

Step2: State the volume formula for a cylinder

$$V = \pi r^2 h$$

Step3: Substitute the given values into the formula

$$V = \pi (8)^2 (10)$$

Step4: Calculate the exact volume in terms of $\pi$

$$V = \pi (64)(10) = 640\pi$$

Step5: Calculate the approximate volume to the nearest whole number

$$V \approx 640 \times 3.14159 \approx 2010.619$$

Answer:

The volume of the figure in terms of $\pi$ is $640\pi \text{ m}^3$. The volume of the figure rounded to the nearest whole number is $2011 \text{ m}^3$.