find the volume of the sphere. give the answer in terms of $\\pi$ and rounded to the nearest cubic…

find the volume of the sphere. give the answer in terms of $\\pi$ and rounded to the nearest cubic foot.\n\nthe volume in terms of $\\pi$ is $v = \\square \\text{ ft}^3$.\n(simplify your answer. type an exact answer in terms of $\\pi$.)

find the volume of the sphere. give the answer in terms of $\\pi$ and rounded to the nearest cubic foot.\n\nthe volume in terms of $\\pi$ is $v = \\square \\text{ ft}^3$.\n(simplify your answer. type an exact answer in terms of $\\pi$.)

Answer

Explanation:

Step1: Identify the radius of the sphere

The image shows a sphere with a radius $r = 6\text{ ft}$.

Step2: State the volume formula for a sphere

The formula for the volume $V$ of a sphere is: $$V = \frac{4}{3}\pi r^3$$

Step3: Substitute the radius into the formula

Substitute $r = 6$ into the equation: $$V = \frac{4}{3}\pi (6)^3$$

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

Calculate $6^3 = 216$, then multiply by $\frac{4}{3}$: $$V = \frac{4}{3} \cdot 216 \cdot \pi = 4 \cdot 72 \cdot \pi = 288\pi$$

Step5: Calculate the approximate volume

Multiply $288$ by $\pi$ ($\approx 3.14159$) and round to the nearest cubic foot: $$V \approx 288 \cdot 3.14159 \approx 904.778$$

Answer:

The volume in terms of $\pi$ is $V = 288\pi\text{ ft}^3$. The volume rounded to the nearest cubic foot is $905\text{ ft}^3$.