Solid Geometry Solutions
Topics || Problems
A solid concrete porch consists of 3 steps and a landing. The steps have a thread of 11 in arise of 7 in and a length of 7 ft.; the landing is 6 ft by 7ft. How much materials were used in its construction?
The materials used in construction is pertaining to the total volume on the porch.
\(V = V_1 + 6V_2\), where \(V, V_1 ~ and ~ V_2\) is the total volume, volume of \(6'x7'\) area and volume of one rectangular parallelepiped step respectively.
\(V_1 = lxwxh = 6x7x\frac{7}{3} = 98\), \(h = \frac{7x4}{12} = \frac{7}{3}'\)
\(V_2 = \frac{11x7}{144} (7)\), convert 11 and 7 inches to ft.
\(V_2 = \frac{539}{144}\)
\(V = 98 + (6) (\frac{539}{144})\)
\(V = 120.46 ~ft^3\) Answer