Question

An artist creates a​ cone-shaped sculpture for an art exhibit. If the sculpture is 8 feet tall and has a base with a circumference of 23.236 ​feet, what is the volume of the​ sculpture? Use 3.14 for pi .

Answer 1

Answer:

The volume of the cone-shaped sculpture is equal to 114.631 ft³.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Geometry

Circumference Formula:
$\displaystyle C = 2 \pi r$

• r is radius

Volume Formula [Cone]:
$\displaystyle V = \frac{\pi r^2 h}{3}$

• r is radius
• h is height

Step-by-step explanation:

Step 1: Define

Identify given.

h = 8 ft

C = 23.236 ft

Step 2: Find Radius r

1. [Circumference Formula] Substitute in variables:
   $\displaystyle \begin{aligned}C = 2 \pi r & \rightarrow 23.236 \ \text{ft} = 2(3.14)r \\\end{aligned}$
2. Solve [Equality Properties]:
   $\displaystyle \begin{aligned}C = 2 \pi r & \rightarrow 23.236 \ \text{ft} = 2(3.14)r \\& \rightarrow r = 3.7 \ \text{ft} \\\end{aligned}$

Step 3: Find Volume

1. [Volume Formula - Cone] Substitute in variables:
   $\displaystyle \begin{aligned}V = \frac{\pi r^2 h}{3} & \rightarrow V = \frac{(3.14)(3.7 \ \text{ft})^2(8 \ \text{ft})}{3} \\\end{aligned}$
2. Evaluate:
   $\displaystyle \begin{aligned}V = \frac{\pi r^2 h}{3} & \rightarrow V = \frac{(3.14)(3.7 \ \text{ft})^2(8 \ \text{ft})}{3} \\& \rightarrow V = \boxed{ 114.631 \ \text{ft}^3 } \\\end{aligned}$

∴ the volume of the artist-created sculpture is 114.631 ft³.

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Learn more about Geometry: brainly.com/question/27732359

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Topic: Geometry