Question

A cone with height h and radius r has volume V= 1/3 πr2 h. If h is 12 in. and V is equal to 47x2−247x+367, what is the cone's radius r in terms of x? A) r=3x−2 B) r=5x−7 C) r=2x−1 D) r=7x−5

Answer 1

Explanation:

To find the cone's radius, we need to rearrange the formula for the volume of a cone. The formula is V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height.

In this problem, we are given that h is 12 inches and V is equal to the quadratic expression 47x² - 247x + 367.

We can equate the given expression for V with the formula for the volume and solve for r. Let's do that:

47x² - 247x + 367 = (1/3)πr²h

Since h is 12, we can substitute it into the equation:

47x² - 247x + 367 = (1/3)πr² * 12

Now, we simplify the equation:

47x² - 247x + 367 = 4πr²

To solve for r, we isolate it on one side of the equation:

4πr² = 47x² - 247x + 367

Divide both sides by 4π:

r² = (47x² - 247x + 367) / (4π)

To find r, we take the square root of both sides:

r = √[(47x² - 247x + 367) / (4π)]

So, the cone's radius r in terms of x is √[(47x² - 247x + 367) / (4π)].

Therefore, the answer is not listed among the options given.