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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 m.
What is the volume of the sphere?
O 6m?
O 7m
O 14m
O 28m​

Sagot :

Baraq

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.

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