Volume and Scale Factor

Question

1. )A map is drawn for a cycling route that is 15 km in length using a scale factor of 0.000002 

     Determine the length of the route on map. 

 

2.) The original volume of a three-dimensional Chef Potato was 1309.0 cm³. What would be the volume of a three-    

 dimensional Chef Potato model with a height that is one quarter that of the original?

  The original height is 20

 

 

3.) Abed is designing an interactive three-dimensional flip calendar to be used on a desktop computer or a tablet.

 

a.) On the screen of a computer monitor, the three-dimensional flip calendar's dimensions are such that it has a surface area of 2100 mm². A scale model of this calendar has a surface area of 52500 mm². Determine the scale factor

 

b.) Determine the scale factor if the volume of the original calendar is 6860 mm³ and the volume of the scale model is 28000 mm^3.

 

c.) The dimensions of a computer are 24 cm (vertical) by 42 cm (horizontal). How many calendar faces with a vertical height of 35 mm and a horizontal width of 28 mm would fit the screen without getting cut off if the original calendar is used as a repetitive background?

Answer 1

1)    .000002 * 15 = .00003 km or 3 cm (I wonder if you got too many zeros in your problem? That's a really small map.)

 

2)  I'm not sure what a chef potato is, but if the small one is geometrically similar to the big one, the ratio of the volumes is the cube of the linear ratio.

 

V₁/V₂ = (1/4)³ = 1/16

 

1/16 = V₁/1309

 

V₁ = 81.8 cm³

 

3a)  Because surface area is a two dimensional measurement, the ratio of the areas is the square of the linear ratio.

 

a₁ / a₂ = 52500 / 2100 = 21 / 1

 

scale = √21 = 4.6

 

3b)  V₁ / V₂ = 28000 / 6860 = 200 / 49

 

     scale = ³√(200/49) = 1.6

 

3c)  I'm not sure what you mean about the repetitive background. But based on the dimensions given:

 

 24 / 3.5 = 6.8 or 6 vertically           42 / 2.8 = 15 horizontally

 

6 * 15 = 90 calendar faces