SOLUTION: a model cylinder fuel tank has a radius of 5cm and a height of 12cm. Scale is 1cm to 1.25m. How tall is the actual fuel tank in meters? 15m? What is the scale factor between mo

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Question 610237: a model cylinder fuel tank has a radius of 5cm and a height of 12cm. Scale is 1cm to 1.25m.
How tall is the actual fuel tank in meters? 15m?
What is the scale factor between model and fuel tank?1/150?
Determine the volume in cubic meters. Determine surface area of the fuel tank in sq m.
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Found 2 solutions by jim_thompson5910, jerryguo41:
Answer by jim_thompson5910(28595) (Show Source):
You can put this solution on YOUR website!
1 cm : 1.25 m

5*1 cm : 5*1.25 m

5 cm : 6.25 m

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1 cm : 1.25 m

12*1 cm : 12*1.25 m

12 cm : 15 m

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So the actual tank has a radius of 6.25 meters and is 15 meters tall

Now convert 15 meters to cm: 15*100 = 1500 cm

Then divide it by 12 cm: 1500/12 = 125

So the scale factor is 1/125

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Volume:

V = pi*r^2*h

V = pi*(6.25)^2*15

V = pi*39.0625*15

V = pi*585.9375

V = 585.9375pi

V = 585.9375(3.14159)

V = 1840.775390625

So the volume of the tank is approximately 1840.775390625 cubic meters

Surface area

SA = 2*pi*r^2 + 2pi*r*h

SA = 2*pi*(6.25)^2 + 2pi*6.25*15

SA = 2*pi*39.0625 + 2pi*6.25*15

SA = 78.125pi + 187.5pi

SA = 265.625pi

SA = 265.625(3.14159)

SA = 834.48484375

and the surface area is approximately 834.48484375 square meters.
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Answer by jerryguo41(162) (Show Source):
You can put this solution on YOUR website!
How tall is the actual fuel tank in meters?
Model: 12cm
12cm*(1.25m/1cm)=15m
Actual:15m
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What is the scale factor between model and fuel tank?
Model: 1cm
Actual: 1.25m or 125 cm
Ration: model/actual -> 1/125
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Determine the volume in cubic meters.
Find Radius of Actual:
Model: 5cm
5cm*(1.25m/1cm)=6.25m
Actual:6.25m
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Volume of Cylinder:V=πr^2*h (r=radius)(h=height)(V=Volume)
V=π6.25^2*15
V=π39.0625*15
V=585.9375π or Approx. 1,839.84 cubic meters
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Surface Area of a Cylinder: Sa=2πr^2+2πr*h (r=radius)(h=height)(Sa=Surface Area)
Sa=2π6.25^2+2π6.25*15
Sa=2π39.0625+2π93.75
Sa=78.125π+187.5π
Sa=265.625π or 834.0625 Square meters