A concrete spherical shell is constructed for building aesthetic. The contractor designated 6 in for its thickness and 24π sq ft for interior area, how much concrete is required for this project?

Question

Solid Mesturation problem. Pleasse Help.

Answer 1

A concrete spherical shell is constructed for building aesthetic. The contractor designated 6 in for its thickness and 24π sq ft for interior area, how much concrete is required for this project?

Let shell radius (outer) = ro

   "     "         "      (inner)  = ri

Then thickness, t = ro – ri = 6 in

 

Volume   (of shell)

Vo = (4/3).pi.ro^3

Vi = (4/3).pi.ri^3

ΔV = Vo - Vi = (4/3).pi(ro^3 - ri^3)

 

Surface Area

Ai = 4.pi.ri^2 

4.pi.ri^2 = 24.pi*(12^2)  square inches

ri^2 = 6*144  

ri = 12√(6) 

 

Using ro – ri = 6

ro = 6 + 12√(6) 

 

ΔV = (4/3).pi(ro^3 - ri^3)

ΔV = (4/3).pi((6 + 12√(6) )^3 – (12√(6) )^3)

ΔV = (4/3).pi((35.394)^3 – (29.394)^3)

ΔV = (4/3).pi(18,942.54)

 

ΔV = 79,346.32 cubic inches = 45.92 cu ft