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8.6 Scale Factors and 3D Shapes (Solutions).notebook November 03, 2015
8.6
Scale Factors
and
3D Shapes
scale factor = k = diagram length
actual length
One Dimension (1D) Length
Two Dimensions (2D) Area
area scale factor = k2 = diagram area actual area
8.6 Scale Factors and 3D Shapes (Solutions).notebook November 03, 2015
Three Dimensions (3D)
Surface Area area scale factor = k2 = diagram area
actual area
Volume volume scale factor = k3 = diagram volume
actual volume
Example 1
The pair of objects is similar.
a) What is the scale factor for the length?
b) For the surface area?
c) For the volume?
6cm
4cm
15cm
10cm
8.6 Scale Factors and 3D Shapes (Solutions).notebook November 03, 2015
Example 2
A small tank has a capacity of 1400 m3, and a similar larger tank has a capacity of 4725 m3.
a) How many times longer will it take to fill the larger tank than it will take to fill the smaller tank?
b) How many times greater is the radius of the larger tank than the radius of the smaller tank?
c) The larger tank is now to be reduced by a scale factor of 0.6 to build another small tank. Determine the capacity of the new small tank.
Example 3A 1:50 model of the world's largest dump truck is shown. The model is 30cm long, 20cm wide, and 15.5cm tall.
a) What are the dimensions of the actual dump truck?
b) The model can carry about 1200cm3 of sand. How much sand can the actual dump truck carry?
8.6 Scale Factors and 3D Shapes (Solutions).notebook November 03, 2015
Example 4
A cylindrical soup can is 10cm wide and 10cm tall. Campbell's wants a can that can hold twice as much soup. What will be the new diameter and height?
p. 508
# 1, 3, 4, 6, 8, 13, 15
8.6 Scale Factors and 3D Shapes (Solutions).notebook November 03, 2015
REVIEWp. 515 # 2, 4, 5, 8, 10, 12, 14 16