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The top of the water tower has a diameter of 20 feet. find the surface area of the top
hm, how many inches are in one foot?
12 i think
yes, so if 0.25 inches on the model tower is 12 inches (or one foot) in real life, how do you get 40 foot on the scale model?
Are we finding the surface area of the model or the actual thing?
ok, well its like saying if 1=0.25 then 40= ?
the top of the actual water tower
Assuming the water tower is a sphere, you know that the SA= 4(pi) r(squared) Therefore, the solution would be SA= 4(pi) (100) =400pi
the water tower is a cylinder
finding the surface area of the model tower
Then how tall is the cylinder?
okay these are all the questions that go with the water tower. 1)You decide that .25 inches in your model will correspond to 12 inches of the actual water tower. what is the scale factor? 2)The top of the water tower has a diameter of 20 feet. find the surface area of the top 3) you decide to make the top of the water tower with silver foil. how many square inches of foil will you need? 4) The height of the actual water tower is 32feet. what is the surface area of your scale model? do not include the base 5) find the volume of the actual water tower 6)use your results from exercise 5 to find the volume of the scale model
2) the surface area of the top is the "circle" that the cylinder ends with which is described by (pi) ((r)(squared)). So the SA= (pi) (10 squared) or 100
do you need help with the other questions?
so #2 is 314ft^2
I think #2 would be 100 pi because you want to find the SA of the top of the cylinder (which ends in a circle). The SA of the top would then be equal to the area of the circle that ends the cylinder. That's given by (pi)((r)(squared)) which is 100pi.
will you please also help with the other questions
i'll do it?
Number 3 is simple. You have the ratio of the scale of the model and the actual tower. You can find the diameter of the top of the model by multiplying (20ft) (12in/ft) (1/48) to get the diameter of the top of the model in inches (which is 5). You then use the same formula A=(pi)(r^2) to get 6.25 pi in^2 of foil needed.
Number 4 is similar. You know the height and the scale between the actual and the model tower... so you find the height of the model by (32ft)(12in/ft)(1/48) to get h=8. You know the SA of the tower will equal the side of the cylinder + the top (which we already know to be 6.25pi in^2 from #3). You can find the SA of the side of the cylinder since it's essentially the circumference of the top circle multiplied by the height. SA= 2(pi)(r)*h + 6.25pi = 40pi+6.25pi=46.25pi in^2