Homework1- For a given soil, show that(1+wsat(Gs+es)Ywa- Ysatb- y == n1+eWsat2- The moist unit weight of a soil is 19.2 kN/m³. Given that G. = 2.69 and w=9.8%, determine:a. Void ratiob. Dry unit weightc. Degree of saturationAns: e=0.51 , Ya=17.48KN/m³ , s=51.7%3- Refer to Problem 2. Determine the weight of water, in kN. to be added per cubic meter (m°) ofsoil fora. 90% degree of saturationb. 100% degree of saturationAns: Water add= 1.25 kN/m³ , 1.58 kN/m³4- For a given soil, the following are known: G, = 2.74, moist unit weight, y = 20.6kN/m², andmoisture content, w = 16.6%. Determine:a. Dry unit weightb. Void ratioc. Porosityd. Degree of saturationAns: Ya = 17.67 kN/m³ e=0.515- It is known that the natural soil at a construction site has a void ratio of 0.92. At the end ofcompaction, the in-place void ratio was found to be 0.65. If the moisture content remainsunchanged, then determine:a. Percent decrease in the total volume of the soil due to compactionb. Percent increase in the field unit weightc. Percent change in the degree of saturationA 2-m-high sandy fill material was placed loosely at a relative density of 47%.Ans: a- 14% decrease6- (5 kg) of soil is at natural water content of 3%. How much water would you add to the above soilto bring the water content to 12%?Ans: Added water = 0.437 kg7- A sandy soil consists of perfectly spherical grains of the same diameter. At the loosest possiblepacking, the particles are stacked directly above each other. Show that the void ratio is 0.910.8- A contractor needs 300 ml of aggregate base for a highway construction project. It will becompacted to a dry unit weight of 19.8 kN/m³. This material is available in a stockpile at a localmaterial supply yard at a water content of 7% but is sold by the metric ton and not by cubicn=0.34S=87.4%b-16.3% increaseC-41.5% increasemeters.a. How many tons of aggregate should the contractor purchase?b. A few weeks later, an intense rainstorm increased the water content of the stockpile to 15%. Ifthe contractor orders the same quantity for an identical section of the highway, how many cubicmeters of compacted aggregate base will he produce?Answer: a- 648 t b-279.2 m39- The bulk unit weight and water content of a soil at a borrow pit are 17.2 kN/ml and 8.2%respectively. A highway fill is being constructed using the soil from this borrow at a dry unitweight of 18.05 kN/m³• Find the volume of the borrow pit that would make one cubic meter of the finished highway fill.Answer: 1.136 m3

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I'm solving Question 1 here for the other parts kindly resubmit the question seperately.

1- For a given soil, show that (1+wsat (Gstes)Yw a- Ysat = n b- y = %3D 1+e Wsat