The volume of a cone is 190 in3. Find a function that models the height h of the cone in terms of its radius r.
190 = pi/3 r^2 h
h = 570 / pi*r^2
Why did the cone go to therapy? It had a lot of unresolved issues with its height and radius!
In order to find a function that models the height of the cone (h) in terms of its radius (r) to solve this problem, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Given that the volume (V) is 190 in^3, we can plug this value into the equation:
190 = (1/3) * π * r^2 * h
To isolate h, we can divide both sides of the equation by [(1/3) * π * r^2]:
h = 190 / [(1/3) * π * r^2]
Simplifying further, we get:
h = 3 * (190 / π * r^2)
So, the function that models the height h of the cone in terms of its radius r is:
h = 3 * (190 / π * r^2)
To find a function that models the height of the cone (h) in terms of its radius (r), we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Given that the volume (V) is 190 in^3, we can plug in this value into the formula:
190 = (1/3) * π * r^2 * h
Now, we can solve for h in terms of r. Let's rearrange the equation:
h = (190 * 3) / (π * r^2)
Therefore, the function that models the height, h, of the cone in terms of its radius, r, is:
h = (570 / (π * r^2))
To find a function that models the height h of a cone in terms of its radius r, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h,
where V is the volume, π is a mathematical constant (approximately 3.14159), r is the radius, and h is the height.
In this case, we know that the volume V is 190 in^3. Substituting this into the formula, we get:
190 = (1/3) * π * r^2 * h.
Now we can solve for h. First, let's simplify the equation:
190 = (1/3) * π * r^2 * h
570 = π * r^2 * h.
Next, we need to isolate h. Divide both sides of the equation by (π * r^2):
570 / (π * r^2) = h.
Therefore, the function that represents the height h of the cone in terms of its radius r is:
h(r) = 570 / (π * r^2).
Note that this function assumes the radius r is positive and nonzero.