If a right circular cone must have a volume of 12 cubic meters, then a function that gives the possible radii as a function of the height is: (The volume of a right circular cone is given by the formula 𝑉=13𝜋𝑟2ℎV= 31 πr 2 h).A.𝑟=36𝜋ℎr= πh36 B.𝑟=±36𝜋ℎr=± πh36 C.𝑟=12𝜋ℎr= πh12 D.ℎ=±36𝜋𝑟2h=± πr 2 36 E.𝑟=36𝜋ℎr= πh36
Question
If a right circular cone must have a volume of 12 cubic meters, then a function that gives the possible radii as a function of the height is: (The volume of a right circular cone is given by the formula 𝑉=13𝜋𝑟2ℎV= 31 πr 2 h).A.𝑟=36𝜋ℎr= πh36 B.𝑟=±36𝜋ℎr=± πh36 C.𝑟=12𝜋ℎr= πh12 D.ℎ=±36𝜋𝑟2h=± πr 2 36 E.𝑟=36𝜋ℎr= πh36
Solution
The volume of a right circular cone is given by the formula V = 1/3 * π * r^2 * h. We know that the volume must be 12 cubic meters, so we can set up the equation 12 = 1/3 * π * r^2 * h.
We want to solve for r, so we first multiply both sides by 3 to get rid of the fraction: 36 = π * r^2 * h.
Next, we divide both sides by πh to isolate r^2: r^2 = 36/(πh).
Finally, we take the square root of both sides to solve for r. Since r is a radius and cannot be negative, we only take the positive square root: r = sqrt(36/(πh)).
Therefore, the function that gives the possible radii as a function of the height is r = sqrt(36/(πh)), which is not listed in the options. There seems to be a mistake in the options provided.
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