I am assuming the both cylinders have the same measure of radius. They only differ in height.
Larger Cylinder = 343 ft³
Smaller Cylinder = 125 ft³ ; height = 5 ft.
We can use proportion for this problem; a:b = c:d where ad = bc
5 ft :125 ft³ = x : 343ft³
5 ft * 343 ft³ = 125 ft³ * x
1715 ft⁴ = 125 ft³ * x
1715 ft⁴ ÷ 125 ft³ = x
13.72 ft = x height of the larger cylinder.
Cone S = 768pi cm³
Cone T = 6144pi cm³ ; height = 24 cm
24 cm : 6144 cm³ = x : 768 cm³
24 cm * 768 cm³ = 6144 cm³ * x
18,432 cm⁴ = 6144 cm³ * x
18,432 cm⁴ ÷ 6,144 cm³ = x
3 cm = x height of Cone S.
