Certainly! Let's go through the problem step-by-step to calculate the volume of a sphere with diameter 11.4 meters using the given value of π (pi) as 3.14, and then round the answer to the nearest tenth.
### Step 1: Understanding the Problem
We are given:
- The diameter [tex]\( D \)[/tex] of the sphere is 11.4 meters.
- We need to use π ≈ 3.14.
- We need to calculate the volume [tex]\( V \)[/tex] of the sphere.
- Finally, round the volume to the nearest tenth.
### Step 2: Find the Radius
The formula for the volume of a sphere is given by:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Where [tex]\( r \)[/tex] is the radius of the sphere. Since [tex]\( D \)[/tex] is the diameter, and the radius is half of the diameter, we have:
[tex]\[ r = \frac{D}{2} \][/tex]
Given that [tex]\( D = 11.4 \)[/tex] meters:
[tex]\[ r = \frac{11.4}{2} \][/tex]
[tex]\[ r = 5.7 \text{ meters} \][/tex]
### Step 3: Calculate the Volume
Now, we plug the radius into the volume formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Substitute [tex]\( r = 5.7 \)[/tex] meters and π ≈ 3.14:
[tex]\[ V = \frac{4}{3} \times 3.14 \times (5.7)^3 \][/tex]
First, calculate [tex]\( (5.7)^3 \)[/tex]:
[tex]\[ (5.7)^3 = 5.7 \times 5.7 \times 5.7 = 185.193 \][/tex]
Next, multiply by π:
[tex]\[ 3.14 \times 185.193 = 581.00722 \][/tex]
Then, multiply by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ \frac{4}{3} \times 581.00722 = 774.6762933 \][/tex]
### Step 4: Round to the Nearest Tenth
To round 774.6762933 to the nearest tenth, we look at the first decimal place. Since this is 7, we round up:
[tex]\[ V \approx 775.3 \][/tex]
### Conclusion
The volume of the sphere, rounded to the nearest tenth, is [tex]\( 775.3 \)[/tex] cubic meters.
