Respuesta :

Answer:

V=804.25

Step-by-step explanation:

r = 8/2

r=4

V=πr^2h

V = π (4)^2 * 16

V =256π

V=804.25

Step-by step solution:

We are given:

  • Diameter of cylinder = 8 units
  • Height of cylinder = 16 units

Volume of a cylinder = π(R)²(H)

  • R = Radius of cylinder
  • H = Height of cylinder

To determine the volume of the cylinder, we need to know the radius and the height of the cylinder, according to the formula stated above.

We already know:

  • The height of the cylinder is given.
  • The radius of the cylinder is not provided.

Radius of the cylinder:

Since the diameter of the cylinder is given, the radius is determinable, as we can set up an equation that represents the relationship between the diameter and the radius. Then, we can plug the diameter into the equation and determine the radius of the cylinder.

Now, we already know that the relationship between a diameter and a radius is that the diameter is twice times greater than the radius.

  • ⇒ Diameter = 2(Radius)
  • ⇒ 8 units = 2(Radius)
  • ⇒ 8 units/2 = 2(Radius)/2
  • ⇒ 8 units/2 = Radius = 4 units

Volume of the cylinder:

Now, plug the height and the radius in the "volume of cylinder" formula.

  • ⇒ Volume of a cylinder = π(R)²(H)
  • ⇒ Volume of a cylinder = π(4)²(16)
  • ⇒ Volume of a cylinder = π(16)(16)
  • ⇒ Volume of a cylinder = 256π                     (Volume in terms of π)

Substituting π as 3.14 (Approximate value of π):

  • ⇒ Volume of a cylinder ≈ 256(3.14)                      
  • ⇒ Volume of a cylinder ≈ 803.84 units³   (Volume in numerical form)

Learn more about volume of cylinders: https://brainly.com/question/23359049

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