Questions: Question 4 Given the radius r of a sphere, calculate its volume V using the formula V=(4/3) π r^3. Calculate V when r=8 feet and use π=3.14. Round your answer to two decimal places.

Question 4
Given the radius r of a sphere, calculate its volume V using the formula V=(4/3) π r^3. Calculate V when r=8 feet and use π=3.14. Round your answer to two decimal places.

Transcript text: Question 4 Given the radius $r$ of a sphere, calculate it's volume $V$ using the formula $V=\left(\frac{4}{3}\right) \pi r^{3}$. Calculate $V$ when $r=8$ feet and use $\pi=3.14$. Round your answer to two decimal places.

Solution

Solution Steps

To calculate the volume $ V $ of a sphere given its radius $ r $, we use the formula $ V = \left(\frac{4}{3}\right) \pi r^3 $. We will substitute $ r = 8 $ feet and $ \pi = 3.14 $ into the formula and round the result to two decimal places.

Step 1: Given Values

We are given the radius $ r = 8 $ feet and $ \pi = 3.14 $.

Step 2: Volume Formula

The formula to calculate the volume $ V $ of a sphere is: \[ V = \left( \frac{4}{3} \right) \pi r^3 \]

Step 3: Substitute the Values

Substitute $ r = 8 $ and $ \pi = 3.14 $ into the formula: \[ V = \left( \frac{4}{3} \right) \times 3.14 \times 8^3 \]

Step 4: Calculate the Volume

First, calculate $ 8^3 $: \[ 8^3 = 512 \] Then, multiply by $ \pi $ and $ \frac{4}{3} $: \[ V = \left( \frac{4}{3} \right) \times 3.14 \times 512 = 2143.5733 \]

Step 5: Round the Result

Round the result to two decimal places: \[ V \approx 2143.57 \]