SOLUTION: Water tower as part of a class project, you obtain the responsibility of making a scale model of the water tower in your town. The water tower's diameter is 12 feet and the height

Algebra ->  Volume -> SOLUTION: Water tower as part of a class project, you obtain the responsibility of making a scale model of the water tower in your town. The water tower's diameter is 12 feet and the height       Log On


   

Question 1182647: Water tower as part of a class project, you obtain the responsibility of making a scale model of the water tower in your town. The water tower's diameter is 12 feet and the height is 16 feet. You decide that 0.5 inch in your model will correspond to 12 inches of the actual water tower.
a. What is the scale factor?
b. What is the radius and height of the model?
c. What is the surface area of the model?
d. What is the volumen of the actual water tower?
e. Use your result from Exercise d to find the volume of the model.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
.5 inches corresponds to 12 inches in real life.

the ratio from scale model to real life is 12 feet /.5 inches
the ratio from real life to scale model is .5 inches / 12 feet.

since the diameter in real life is 12 feet, then the diameter on the scale model is .5/12 * 12 = .5 inches.

since the height in real life is 16 feet, then the height on the scale model is .5/12 * 16 = .666666667 = 2/3 inches.

since the diameter in the model is .5 inches, then the radius in the model is half that = .25 inches on the scale model; 6 inches in real life.

the questions are:

a. What is the scale factor?

the scale factor from the model to real life is .5 inches for each 12 feet = .5/12.
the scale factor from real life to the model is 12 feet for each .5 inches = 12/.5

b. What is the radius and height of the model?

the radius of the model is .5/12 * 6 = .25 inches
the height of the model is .5/12 * 16 = 2/3 inches.

c. What is the surface area of the model?

S = surface area = 2*pi*r^2 + 2*pi*r*h
in the model, S = 2*pi*.25^2 + 2*pi*.25*2/3 = 1.439896633 square inches.

d. What is the volume of the actual water tower?

V = pi*r^2*h
in real life, V = pi * 6^2 * 16 = 1809.557368 cubic feet.

e. Use your result from Exercise d to find the volume of the model.

the volume of the model is pi * .25^2 * 2/3 = .1308996939 cubic inchea.

if the ratio of the sides is .5/12, then the ratio of the volume is (.5/12)^3 = 7.233796296 * 10^-5.
since the volume in real life is 1809.557368, then the volume of the model is expected to be 7.233796296 * 10^-5 * that = .13089969390.

this confirms that the ratio of the volume from real life to the model is correct.

note that the ratios are inches to feet and feet to inches.
the model is in inches; real life is in feet.