A cone with height h and radius r has volume V = 13πr^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?

Answer 1

The first answer is definitely the route you should take. However, it is missing the coefficient part of the Volume formula. V = 1/3 π r² h.

I should also add that the formula in your problem states 13 as it should probably be 1/3.

3πx² + 42πx + 147π = 1/3 π r² (9)

Divide both sides by π:

3x² + 42x + 147 = 1/3 r² (9)

When consolidating, your 9 and 1/3 on the right can be combined to equal 9/3, or 3. Then divide by 3 and take the square root to get r by itself.

3x² + 42x + 147 = 3r²

x² + 14x + 49 = r²

^

r = √(x² + 14x + 49)

r = (x + 7) (x + 7)

Answer 2

V=∏r^2h

9∏r^2=3∏x^2+42∏x+147∏

divide both sides by ∏

9r^2=3x^2+42x+147

divide both sides by 9

r^2=x^2/3+14x/3+49/3

r^2=(x^2+14x+49)/3

r^2=(x+7)^2/3

take the square root of both sides

r=(x+7)/√3

r=(x+7)√3/3