Alright, Nela wants to find the volume of her circular backyard swimming pool, which is effectively a cylinder. The radius (r) of the pool is 5 feet and the height (h) is 6 feet. To find the volume (V) of a cylinder, we use the formula:
[tex]\[ V = \pi r^2 h \][/tex]
We need to substitute the given values into this formula step-by-step. Let me guide you through this.
1. Identify the given values:
- Radius (r) = 5 feet
- Height (h) = 6 feet
- π (pi) is approximately 3.14
2. Substitute these values into the formula:
- [tex]\( r^2 \)[/tex] means we need to square the radius:
[tex]\[ r^2 = 5^2 = 25 \][/tex]
- Next, use the formula for the volume:
[tex]\[ V = 3.14 \times 25 \times 6 \][/tex]
3. Multiply the values step-by-step:
- Multiply [tex]\( 3.14 \)[/tex] by [tex]\( 25 \)[/tex]:
[tex]\[ 3.14 \times 25 = 78.5 \][/tex]
- Now multiply this result by the height, [tex]\( 6 \)[/tex]:
[tex]\[ 78.5 \times 6 = 471.0 \][/tex]
So, the correctly substituted and calculated volume for Nela's swimming pool is [tex]\( 471.0 \)[/tex] cubic feet.
Therefore, the appropriate substitution step-by-step would look like:
[tex]\[ V = 3.14 \times 5^2 \times 6 = 3.14 \times 25 \times 6 = 471.0 \text{ cubic feet} \][/tex]
This shows the correct substitution and the true volume calculation.
