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A welder is commissioned to make a gold metal cone from a cylindrical cone form, as shown. The height of the cylinder is 66 centimeters, and the diameter of the cylinder is 20 centimeters. The welder purchases tubs of material to fill up the shaded portion of the form to make the gold cone. The formula for the volume of a cone is V = 1 3 π r 2 h , while the formula for the volume of a cylinder is V = π r 2 h .

Respuesta :

The shaded portion is equal to 13816cm^3

Data;

  • Height = 66cm
  • d = 20cm

Volume of a Cylinder

The formula of volume of a cylinder is given as

[tex]v=\pi r^2 h[/tex]

Let's substitute the values and solve

[tex]v = \pi r^2 h\\\\r = d/2\\d = 20\\r = 20/2 = 10cm\\v = 3.14 * 10^2 * 66\\v = 20724cm^3[/tex]

Volume of a Cone

The volume of a cone is given as

[tex]v = 1/3 \pi r^2 h\\v = 1/3 * 3.14 * 10^2 * 66\\v = 6908cm^3[/tex]

The space remaining from creating the cone out of the cylinder is

[tex]20724 - 6908 = 13816cm^3[/tex]

The shaded portion is equal to 13816cm^3

Learn more on volume of cone and cylinder here;

https://brainly.com/question/25920983

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