1) A cylidrical underground storage tank with a radius of 10.0 feet and a height of 40.0 feet is filled with gasoline. Given a density of 670 kg/m^3, determine the mass of the gasoline in the tank. If the average automobile gas tank holds 25.0 gallons, compute the number of autos that may be filled from this underground facility.
Solution:
In this problem do not forget to convert feet to meters. 10feet =3.048 meters 40 feet = 12.192 m
The volume of the cylinder is
And since 1 gallon is 0.003785 cubic meters and hence 25 gallons is 0.0946 cubic meters than the number of cars will be
Answer: 355.66m^3 and 3759 autos
2) In 1968 Flagstaff recieved a tremedous amount of snow. To remove the snow from the city streets, it was piled on frozen lake Mary. Assuming that the snow stood on the frozen lake in a perfect cone with a base diameter of 200.0 feet and a height of 18.00 feet, determine: a) the volume of the pile b) the mass of the snow (the density is 850 kg/m^3) c) the force that the snow exerted on Lake Mary in N and in lbf
Volume of the cone is given by
The mass id then
The force
To convert Newtons to lbf I used the fact that 1 N = 0.2248 lbf
3) The change in pressure across a partial blockage in an artery, called a stenosis, can be approximated by the following equation, where: p2-p1=Kv(u)v/d+Ku(Ao/A1+1)^2p(v^2) where: p1,p2=pressure,N/m^2 V=blood velocity,m/s u=blood viscosity, N s/m^2 P=blood density, in kg/m^3 D= artery diameter A0=area of unobstructed artery, m^2 A1=area of stenosis, m^2. Determine the dimensions of the constants Kv and Ku in both the SI system and the US customary system.
Denoting by x dimensions for Ku can be instantly obtained as Pa/m = x*Pa*m^2/s^2 è x = s^2/m and in US it will be s^2/ft
Regarding Kv since units for viscosity is Pa*s and units for v/d = 1/s we get
Pa/m = x*Pa*s/s è x = 1/m or in US 1/ft
Answer: unit for Kv are 1/m, and 1/ft for Ku s^2/m and s^2/ft
4) A construction company is looking into purchasing the plot of a land, and dividing it into 2-acre lots for a housing development. The parcel is formed by the intersection of three roads and a lake. Payne Road intersects US 19 at an angle of 58 degrees and US 19 intersects Green Belt Drive at 98 degrees. The distance between points A and B is 875 yards, points B and C is 1000 yards, and points C and D is 955 yards. (a) find the distance between points A and D in feet. (b) Find the total area in square feet of the land bordered by the four points. Disregarg the irregular coastline. (c) Determine how many 2-acre plots can be sold in the development. (d) If the lots bordering the lake have a minimum of a 200 foot frontage and sell for $65,000 each and the other lots all sell for $43,000, what is the total value of the lots in the development?
For this one I need to know where are A and B points can you attach a graph