To find the height of a cone given its volume and radius, we can use the formula for the volume of a cone, which is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height of the cone.
a. If the cone's radius is 1 and the volume is 3π:
3π = (1/3)π(1)^2h
3 = (1/3)h
9 = h
b. If the cone's radius is 2 and the volume is 3π:
3π = (1/3)π(2)^2h
3 = (4/3)h
h = 9/4
c. If the cone's radius is 5 and the volume is 3π:
3π = (1/3)π(5)^2h
3 = (25/3)h
h = 9/25
d. If the cone's radius is r and the volume is 3π:
3π = (1/3)π(r)^2h
3 = (r^2/3)h
h = 9/r^2
So, the height of the cone varies depending on the radius and the given volume.
