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the south African large telescope (SALT) is housed in a cylindrical building with a doomed roof in the shape of a hemisphere. The height of the building wall is 17 m and the diameter is 26m. To program the ventilation system for heat, air conditioning, and dehumidifying, the engineers need the amount of air in the building. What is the volume of air in the building ?

the south African large telescope SALT is housed in a cylindrical building with a doomed roof in the shape of a hemisphere The height of the building wall is 17 class=

Respuesta :

Solution

Height (h) = 17m

Diameter (d) = 26m

Radius (r) = d/2 = 26/2 = 13m

The Volume will be

[tex]Volume=Volume\text{ }Of\text{ }Cylindrical\text{ }Body+Volume\text{ }Of\text{ }Hemisphere[/tex]

So,

[tex]\begin{gathered} Volume\text{ }Of\text{ }Cylinder=\pi r^2h \\ \\ Volume\text{ }Of\text{ }Cylinder=\pi\times13^2\times17 \\ \\ Volume\text{ }Of\text{ }Cylinder=2873\pi \end{gathered}[/tex]

and

[tex]\begin{gathered} Volume\text{ }Of\text{ }Hemisphere=\frac{2}{3}\pi r^3 \\ \\ Volume\text{ }Of\text{ }Hemisphere=\frac{2}{3}\times\pi\times13^2 \\ \\ Volume\text{ }Of\text{ }Hemisphere=\frac{338}{3}\pi \end{gathered}[/tex]

The volume of the air in the building is

[tex]\begin{gathered} Volume=2873\pi+\frac{338}{3}\pi \\ \\ Volume=\frac{8957}{3}\pi \\ \\ Volume=9379.748466m^3 \\ \\ Volume=9379.75m^3\text{ \lparen to two decimal places\rparen} \end{gathered}[/tex]

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