Answer:
14m³
Explanation:
Considering the Volume of the cylinder = 21m³
Hence, to find the Volume of the sphere
We have V = πr²h
Substitute 21 for V; this gives
21 = πr²h
Divide both sides by h
We have 21÷h = πr2h ÷ 2
21÷h = πr2h
Solve for the volume of the sphere using the given formula;
V= (4/3πr3) ÷ 3
Divide both sides by r
=> V/3 = (4/3πr3) ÷ 3r
Expand the equation
=> V/3 = (4/3πr2) ÷ 3
Then substitute 21÷h = πr²
= V/r = 4/3 * 21/h
=> V/r = 84/3h.
V/r = 28/h
Multiply both sides by r
=> r * V/r = 28/h * r
Hence, we have V = 28r/h (eqn)
Based on the question given that the height of the cylinder and the sphere have equal value;
Hence, we have here
h = D represents the diameter of the sphere
Therefore we have D =2r.
=> h = D = 2r
h = 2r
Hence, substitute 2r for h in equation 1
V = 28r/ 2r
V = 28/2
V = 14.
Therefore, the final answer is 14.
