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The American Heritage Center at the University of Wyoming is a conical building. If the height is 77 feet, and the area of the base is about 38,000 square feet, find the volume of air that the heating and cooling systems would have to accommodate.

Remember the formulas

Volume of a cylinder = πr^2h
Volume of a cone = πr^2h/3
Volume of a circle = πr^2
Volume of a sphere = (4/3)πr^3​

Respuesta :

The volume of the cone is 35069.35ft^3 which is equivalent to the air the heating and cooling system would accommodate

Data;

  • Height = 77 feet
  • Area = 38,000 ft^2
  • Volume of a Cone = ?

Volume of a Cone

The shape of a cone has a spherical base. From the given data, we can find radius of the sphere from this.

[tex]A = \frac{4}{3}\pi r^3\\38000 = \frac{4}{3}* 3.14 * r^3\\4.186r^3 = 38000\\r^3 = \frac{38000}{4.186} \\r^3 = 9077.878\\r = \sqrt[3]{9077.878} \\r = 20.86ft[/tex]

The volume of a cone is given as

[tex]v=\frac{1}{3} \pi r^2 h\\v = \frac{1}{3} * 3.14 * 20.86^2 * 77\\v = 35069.35ft^3[/tex]

The volume of the cone is 35069.35ft^3

Learn more on volume of a cone here;

https://brainly.com/question/15321521

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