Answer:
The volume of the cone-shaped sculpture is equal to 114.631 ft³.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Algebra I
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Geometry
Circumference Formula:
[tex]\displaystyle C = 2 \pi r[/tex]
Volume Formula [Cone]:
[tex]\displaystyle V = \frac{\pi r^2 h}{3}[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
h = 8 ft
C = 23.236 ft
Step 2: Find Radius r
- [Circumference Formula] Substitute in variables:
[tex]\displaystyle \begin{aligned}C = 2 \pi r & \rightarrow 23.236 \ \text{ft} = 2(3.14)r \\\end{aligned}[/tex] - Solve [Equality Properties]:
[tex]\displaystyle \begin{aligned}C = 2 \pi r & \rightarrow 23.236 \ \text{ft} = 2(3.14)r \\& \rightarrow r = 3.7 \ \text{ft} \\\end{aligned}[/tex]
Step 3: Find Volume
- [Volume Formula - Cone] Substitute in variables:
[tex]\displaystyle \begin{aligned}V = \frac{\pi r^2 h}{3} & \rightarrow V = \frac{(3.14)(3.7 \ \text{ft})^2(8 \ \text{ft})}{3} \\\end{aligned}[/tex] - Evaluate:
[tex]\displaystyle \begin{aligned}V = \frac{\pi r^2 h}{3} & \rightarrow V = \frac{(3.14)(3.7 \ \text{ft})^2(8 \ \text{ft})}{3} \\& \rightarrow V = \boxed{ 114.631 \ \text{ft}^3 } \\\end{aligned}[/tex]
∴ the volume of the artist-created sculpture is 114.631 ft³.
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Learn more about Geometry: https://brainly.com/question/27732359
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Topic: Geometry
