Height: The volume of a cone is 100 in^3. Find a function that models the height h of the cone in terms of its radius r.
The volume of a cone is given by
V=pixr^2xh/3
Thus 100=pixr^2xh/3
which you need to rearrange to make h the subject.
Find the volume of a cone with radius 26.8 inches and height 31.7 inches. Round the answer to one decimal place.
To find a function that models the height of a cone in terms of its radius, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Given that the volume of the cone is 100 in^3, we can substitute V = 100 and solve for h:
100 = (1/3) * π * r^2 * h
We can rearrange the equation to solve for h:
h = 3 * (100 / (π * r^2))
Thus, a function that models the height h of the cone in terms of its radius r is:
h(r) = 3 * (100 / (π * r^2))