Answer:
Explanation:
The volume of a cylinder with height "h" and radius "r" is given by the formula: V = πr^2h.
The volume of a cone with height "h" and radius "r" is given by the formula: V = (1/3)πr^2h.
To find the volume of a cone with the same height and radius as a cylinder with a volume of 234 cubic inches, we need to find the height and radius of the cylinder. We can use the volume formula for the cylinder to do this:
V = πr^2h
234 = πr^2h
Dividing both sides by πr^2:
h = 234 / (πr^2)
Now that we know the height, we can use it to find the radius using the volume formula for the cylinder:
234 = πr^2h
Taking the square root of both sides:
r = √(234 / πh)
Finally, we can use the height and radius to find the volume of the cone:
V = (1/3)πr^2h
This answer will give us the volume of a cone with the same height and radius as a cylinder with volume 234 cubic inches.