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A cone with height h and radius r has volume V = 1/3πr^2h. If a certain cone with a height of 9 inches has volume V = 3πx^2 + 42πx + 147π, what is the cone’s radius r in terms of x?

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ElenaRisk1569288

Answer:

U should thank me. I went up to 100 pages in my book to find this!!!

Step-by-step explanation:

The volume of a cone is given by: V = π ∙ r2 ∙ h / 3, where π ∙ r2 is the base area of the cone. π defines the ratio of any circle's circumference to its diameter and is approximately equal to 3.141593, however the value 3.14 is often used. Hope u have a nice day and a safe one!:)

akposevictor

The radius of the cone in terms of x is: r = √(x^2 + 14x + 49).

What is the Volume of a Cone?

Volume of cone (V) = 1/3πr²h, where r is the radius and h is the height of the cone.

Given:

h = 9 in.

V = 3πx^2 + 42πx + 147π

r = ?

Substitute

3πx^2 + 42πx + 147π = 1/3(π)(r²)(9)

3π(x^2 + 14x + 49) = (π)(r²)(3)

Divide both sides by 3π

x^2 + 14x + 49 = r²

Square both sides

√(x^2 + 14x + 49) = r

r = √(x^2 + 14x + 49)

Therefore, the radius of the cone in terms of x is: r = √(x^2 + 14x + 49).

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https://brainly.com/question/13677400

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