An embankment for a highway project in Assam is to be constructed to facilitate an overpass over an important junction. To calculate the volume of earthwork required for its preparation, the engineer divides it in to 5 number of sections at a common interval of 10 m. If the total volume of earthwork calculated by Simpon’s 1/3 rd Rule is 3500 m 3 , then the area of the fifth section (in m 2 ) will be ________. (The area of 1 st , 2 rd , 3 rd and 4 th section is found to be 32 m 2 , 64 m 2 , 80 m 2 and 96 m 2 respectively)

Concept: Volume of earthwork by Simpon’s 1/3 rd Rule can be calculated as: \({\rm{V}} = \frac{1}{3} \times \left[ {\left( {{{\rm{A}}_1} + {{\rm{A}}_{\rm{n}}}} \right) + 4\left[ {{{\rm{A}}_2} + {{\rm{A}}_{{4^ + }}}} \right] + 2\left[ {{{\rm{A}}_3} + {{\rm{A}}_5} + ..\; \ldots \ldots } \right]} \right]\) Where, d = interval between two sections, A 1 = Area of section 1, A n = Area of last section, A 2 , A 4 = Even number of area section, and A 3 , A 5 = Odd number of area section Calculation: Given: d = 10 m, A 1 = 32 m 2 , A 2 = 64 m 2 , A 3 = 80 m 2 , A 4 = 96 m 2 , and V = 3500 m 3 \(\because 3500 = \frac{{10}}{3} \times \left[ {\left( {32 + {{\rm{A}}_5}} \right) + 4\left( {64 + 96} \right) + 2 \times 80} \right]\) ∴ A 5 = 218 m 2