Respuesta :
Answer:
[tex]185553.7\text{ feet}^3[/tex]
Step-by-step explanation:
GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is [tex]84\text{ feet}[/tex], and the total height of the building up to the top of the dome is [tex]91\text{ feet}[/tex].
TO FIND: what is the approximate total volume of the building.
SOLUTION:
let the height of the mountaintop be [tex]h\text{ feet}[/tex]
As the dome hemispherical.
circumference of a hemisphere [tex]=\frac{1}{2}\times2\pi\times radius[/tex]
[tex]=\pi\times radius[/tex]
[tex]\frac{22}{7}\times radius=84[/tex]
[tex]radius=26.75\text{ feet}[/tex]
total height of the building up to the top of the dome [tex]=\text{radius of hemisphere}+\text{height of mountaintop}[/tex]
[tex]=26.75+h=91[/tex]
[tex]h=64.25\text{ feet}[/tex]
Volume of building [tex]=\text{volume of cylindrical mountaintop}+\text{volume of dome}[/tex]
[tex]=\pi(radius)^2h+\frac{2}{3}\pi(radius)^3[/tex]
as radius of mountain top is same as dome
putting values
[tex]=3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3[/tex]
[tex]=145484.6+40069.1[/tex]
[tex]185553.7\text{ feet}^3[/tex]
Hence the total volume of the building is [tex]185553.7\text{ feet}^3[/tex]
