ume it takes 10.0 min to ran a 25.0-g gasoline tank. (1 uss. gal 231 in a) Calcu

Question

ume it takes 10.0 min to ran a 25.0-g gasoline tank. (1 uss. gal 231 in a) Calculate the rate at which the tank is filled in gallons per second b) Calculate the rate at which the tank is filled in cubic meters per second c) Determine the time intgrval, in hours, required toa i.00 m, volume at the same rata, (1 us gal " 231 in Need Help?ehWoh My N One otk meter (1.00 m, of alam inum has a mass of 2.70g) ka, and the same va med i on Nao mas balante a solid iron sphhere of radius 2.08 cm on an equal-arm balance M6 x 10. kg tin the rad usoa Id al nor phere the Nood Help? Noles Ask Your T One 9alunofpaint (volem"-3. 7. x 10 , m,) covers an area 20.0 m,, what ana ttia nee,of the fein pant et he walD

Explanation / Answer

4

(a)

Given data:

volume of gasoline tank = 25 gal.

time taken = 10 min. = 600 seconds

rate in gal/sec = 0.0416 gal/s

(b)

1 inch3 = 1.6387 x 10-5

1 gallon = 231 inch3

25 gallon = 0.094635 m3

rate = 0.094635/600 = 1.577 x 10-4 m3/s

(c)

rate = 1.577 x 10-4 m3/s

to fill 1 m3 = 1/1.577 x 10-4

t = 6340.14 seconds

t = 1.76 h

5

density = mass / volume

For aluminum:
d = (2.7 x103 kg)/(1.00 m3) = 2.7 x 103 kg/m3

For iron:
d = (7.86 x103 kg)/(1.00 m3) = 7.86 x 103 kg/m3

Find the volume of the iron sphere.
V = (4/3) pi* r3

V = (4/3)(3.14)(0.0208 m)3
V = 3.7675 x 10-5 m3

m = d*V = (7.86 x 103 kg/m3)( 3.7675 x 10-5 m3 )

m = 0.296 kg  

V = m/d = (0.296 kg)/( 2.7 x 103 kg/m3) = 1.09677 x 10-4 m3

V = (4/3) pi* r3
3/(4*pi) * V = r3
r3 = 3/(4*3.14) * 1.09677 x 10-4 m3

r3 = 2.61968327 x 10-5 m3
r = 0.0296 m
r = 2.96 cm

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