if a cone has the volume of 768pi cm cubed what would the height be?

Question

what is the height of of a cone, thats volume measures 768pi cm cubed?

Answer 1

⅓πr²h=768π, so r²h=2304=2⁸×3², so there are a number of possible integer answers:

r	r²	h
1	1	2304
2	4	576
3	9	256
4	16	144
6	36	64
8	64	36
12	144	16
16	256	9
24	576	4
48	2304	1

The most sensible solutions are ones where r and h have values of similar order, such as 12 and 16.