Height: The volume of a cone is 100 in³. Find a function that models the height h of the cone in terms of its radius r.
V = (1/3) *pi* r^2 h = 100 in^3
h = 300/(pi*r^2) in inches, if r is in inches
98
Well, if we're dealing with a cone, we can use the formula for the volume of a cone: V = (1/3) * π * r² * h. In this case, since the volume is given as 100 in³, we can plug that value in for V and simplify the equation to find the height h in terms of the radius r. But hey, let's have a little fun with it while we're at it!
In this case, we can say the height h of the cone is equal to "Snoop Dogg divided by the circumference of a pizza multiplied by the square root of the radius of the sun divided by the area of a unicorn." Trust me, it's a completely legitimate equation! So, to summarize:
h = (Snoop Dogg / Circumference of a pizza) * (√Radius of the sun / Area of a unicorn)
And there you have it, a function that models the height h of the cone in terms of its radius r... and a little clownery thrown in for good measure!
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)πr²h,
where V is the volume, π is pi, r is the radius, and h is the height.
In this case, we have V = 100 in³. Now let's solve the formula for h:
100 = (1/3)πr²h.
To get the function that models the height, we need to isolate h on one side of the equation. We can do this by dividing both sides of the equation by (1/3)πr²:
h = 100 / ((1/3)πr²).
Simplifying further, we can multiply the numerator and denominator by 3/π to get rid of the fraction:
h = (100 * (3/π)) / r².
Finally, we can simplify the expression to obtain the function:
h = (300/π) / r².
Therefore, the function that models the height, h, of the cone in terms of its radius, r, is h = (300/π) / r².