2 Shift 1. A project you are working on requires 225 nuts and 225 bolts. The pro

Question

2 Shift 1. A project you are working on requires 225 nuts and 225 bolts. The properly-sized nuts are square with 15.0 mm sides and are 4.0 mm thick. The round hole in the middle is 8.0 mm in diameter. How many 0.75-lb boxes of nuts do you need to buy if they are made of a metal with a density of 7.88 g/cm? Assume a classmate graciously donated the bolts from their own personal supply 2. Suppose a particular anabolic steroid may be detected in a human blood sample in quantities as low as 3.6 ng/ul. An athlete injects himself with 193x 10' oz of the steroid just before a competition. If the athlete's blood volume is 2.12 gallons, will the quantity of steroid in the athlete's bloodstream be detectable? (Make sure you check your prefixes (e.g. nano (n-) vs. micro (-) !)

Explanation / Answer

Solution :-

Q1) Lets first calculate the volume of squares

Volume of square =leght * height * width

                                 = 15.0 mm * 15.0 mm * 4.00 mm

                                  = 900 mm^3

900 mm^3* 1 cm^3 / 1000 mm^3 = 0.900 cm^3

Now lets calculate the volume of the hole (cylinder) in the square

Volume of cylinder =pi r^2h

Radius r = diameter /2

                = 8.00 mm /2

                 = 4.00 mm

Volume = 3.14 * (4.00mm)^2*4.00 mm

               = 201 mm^3

201 mm3 *1cm3/ 1000 mm3 = 0.201 cm3

Volume of nut = volume of square – volume of hole

                          = 0.900 cm3 – 0.201 cm3

                          = 0.699 cm3

Now lets calculate mass of 1 nut

Mass = volume x density

         = 0.699cm3 * 7.88 g/cm3

         = 5.508 g

1 box = 0.75 lb

0.75lb *453.592 g / lb = 340.2 g

Now lets calculate the number of nuts in 1 box

Number of nut in box = mass of box / mass of nut

                                        = 340.2 g / 5.508 g

                                        = 62 nut /box

Now lets calculate the number of box needed to get 225 nuts

# of box = 225 nuts / 62 nut per box

               = 3.63 box

So we can round 3.63 box to integer number as 4.0 box

Hence 4.0 box of nuts need to buy.

Q2) mass of steroid injected = 1.93*10^-3 oz

1.93*10^-3 oz * 2.835*10^10 ng / 1 oz = 5.47*10^7 ng steroid

Volume of blood = 2.12 gallon

Lets convert gallon to microliter

2.12gallon * 3.785*10^6 uL/1 gal = 8.02*10^6 uL

Now lets calculate the concentration of the steroid

Concentration of steroid in the athlete body = mass of steroid / volume of blood

                                                                               = 5.47*10^7 ng / 8.02*10^6 uL

                                                                               = 6.82 ng/uL

The concentration of the steroid in the athlete body is higher than detectable amount which is 3.6ng/uL

Therefore the quantity of steroid in the athlete body can be detected.

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