You and your friends decide to make a scale model of the water tower in your town. your scale factor is 1:48. the top of the water tower has a diameter of 20feet. the surface area of the top is 314ft^2. You decide to make the top of the water tower with silver foil. How many square inches of foil will you need?? The height of the actual water tower is 32 feet. What is the surface area of your scale model? Do not include the bottom base. Find the volume of the actual water tower? Use your result of the volume of the actual water tower, to find the volume of the scale model.
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This look like an example of a problem with "false context". What shape is the water tower assumed to have?
There's a couple of problems to solve here. One thing to keep in mind is that "scale factor" applies to dimensions, not to area/volume. So the process here would be:
1) Given the area or volume of the actual water tower find the radius.
2) Scale height/radius by the given factor
3) Calculate the areas using newly obtained dimensions.
You'll have to pay attention to conversion between square feet to square inches too.
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yes very true
would this be right..
1 ft = 12 in, so 20 ft = 240 in
Radius = diameter / 2 = 240 in / 2 = 120in for the real deal.
The model has a radius of 120 in • 1/ 48 = 120in / 48 = 2.5 in
A (base) = (2.5)² • π
A = 6.25π
A ≈ 19.635 in²
I need approx 19.635 in² of foil
32 ft = 384 in
384 in / 48 = 8 in
SA = 2π r² + 2π rh = 2πr(r + h)
SA = 2 π (2.5) (2.5 + 8)
SA = 2 π (2.5) (10.5)
SA = 5 π (10.5)
SA = 52.5 π
SA ≈ 164.93in²
We do not want to bottom base, so 164.93in² - 19.635 in² = 145.295 in²
The surface area is approx. 145.295in².
V = (πr²)h
V = (19.635 in² )8 in
V ≈ 157.01 in²
The volume is approx. 157.01 in²