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An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 8 feet tall and has a base with a circumferen

Andreas93 [3]

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

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

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

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

6 0

2 years ago

Which of the following statements are true about the graph. check all that apply?

oee [108]

Answer:

Statement 1

The graph has a minimum.

This statement is true. The graph has a minimum at x = -1 that is f(-1) = -9.

Statement 2

The graph has a maximum.

The statement is false. As there is no downward curve nor a rigid endpoint but the graph is continuous in upward direction.

Statement 3

The graph has zeros of -4 and 2.

The statement is true because f(-4) = 0 and f(2) = 0.

Statement 4

The vertex is located at (-1, -9).

The statement is true as apparent in the graph.

Statement 5

The solution of the quadratic function represented by the graph is (-1, -9).

The statement is false. Solution of the graph is at the point where f(x) becomes zero. At (-1,-9), f(x) = -9. Hence solution is not at point (-1,-9).

Statement 6

The y-intercept of the graph is (0, -8).

The statement is true. y-intercept of a graph is where the graph intercept the y-axis which means x = 0. As x = 0 at (0, -8), it is the y-intercept of the graph.

8 0

3 years ago

Ken paid 412 for two magazines. The cost of each magazine was multiple of 43. What are the possible prices of the magazines

andrew11 [14]

I'm guessing you mean magazines as in bullets. Well, if he paid $412 dollars for two, and each were sold as a multiple of 43. Then each bullet was $4.79.

You find this by dividing 412 by 2 which gives you $206.

Now divide that by 43. Which is $4.79 (.ea) bullet.

5 0

3 years ago

Read 2 more answers

What is the diameter of this circle if the circumference is 30 x inches?

ch4aika [34]

Answer:

<h2>10 inches</h2>

Step-by-step explanation:

Given the circumference= 30 in

we know that the formula for circumference is

$C= 2\pi r$