A cone has a volume of 600 pi inches cubed. Find two possible sets of dimensions for the height and radius of the cone.

V= (1/3)π r^2 h

600π = (1/3)πr^2h
1800 = r^2 h
h = 1800/r^2

pick any r value you feel like, then evaluate h
e.g. r = 9
h = 1800/81 = 200/9 or 22.22..

find as many as you want

To find two possible sets of dimensions for the height and radius of a cone with a given volume, we need to use the formula for the volume of a cone.

The formula for the volume of a cone is V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cone is 600π inches cubed. Thus, we have the equation:

600π = (1/3)πr²h

To find two possible sets of dimensions, we need to choose different values for the radius and height that satisfy this equation.

Set 1:
Let's assume the radius (r) is 10 inches. We can substitute this value into the equation:

600π = (1/3)π(10)²h

Simplifying the equation:

600π = (1/3)π(100)h
600 = (1/3)(100)h
600 = 33.33h

Dividing both sides by 33.33:

h ≈ 18

So, one possible set of dimensions for this cone is a radius of 10 inches and a height of 18 inches.

Set 2:
Now, let's assume the radius (r) is 5 inches. We can substitute this value into the equation:

600π = (1/3)π(5)²h

Simplifying the equation:

600π = (1/3)π(25)h
600 = (1/3)(25)h
600 = 8.33h

Dividing both sides by 8.33:

h ≈ 72

Therefore, another possible set of dimensions for this cone is a radius of 5 inches and a height of 72 inches.