# An observatory is to be in the form of a right circular cylinder surmounted by a hemispherical dome. If the hemispherical dome costs 5 times as much per square foot as the cylindrical wall, what are the most economic dimensions for a volume of 4000 cubic?

##### 1 Answer

Radius oh dome = 5.28'= 5'3.4'', nearly, and the height of the cylinder = 42.15' = 42'2'', nearly

#### Explanation:

Let r' = the radius of the dome and h' = the height of the right circular

cylinder and cost per square foot surface area = 1 unit of cost. Then,

Volume enclosed

#h =.(4000/(pir^2)-2/3r)'.

Cost

Eliminating h,

For minimum C, C' = 0. So,

#=.42.15'.