Question

DUE IN 20 MINUTES AND I DON'T KNOW HOW TO SOLVE!

A cone with height h and radius r has volume V = 13πr2h. If a certain cone with a height of 9 inches has volume V = 3πx2 + 42πx + 147π, what is the cone’s radius r in terms of x?

Answer 1

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

Step-by-step explanation: 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)