If two figures are similar then:
Surface area of similar figures :
If the corresponding sides of similar figures are in the ratio k, then :
Area of image = k^{2} x area of object.
Volume of similar figures :
If the corresponding sides of similar solids are in the ratio k, then:
Volume of image = k^{3} x volume of object.
Are the two figures similar ? If so, state the scale factor.
Problem 1 :
Solution :
Comparing the corresponding sides, we get
80k = 24 k = 24/80 k = 3/10 |
60k = 18 k = 18/60 k = 3/10 |
40k = 12 k = 12/40 k = 3/10 |
Since the ratios are equal, the given shapes are similar. The scale factor is 3 :10.
Problem 2 :
Solution :
Comparing the corresponding sides,
40/8 = 5
50/20 ≠ 5
Since the ratios are not same, the shapes are not similar.
Problem 3 :
Solution :
81k = 27 k = 27/81 k = 1/3 |
54k = 18 k = 18/54 k = 1/3 |
Since the ratios are same, the shapes are similar. The required scale
factor is 1 : 3.
Problem 4 :
Solution :
Comparing the corresponding sides,
18/54 = 1/3
6/21 = 2/7
Since the ratios are not same, they are not similar shapes.
Each pair of
figures is similar. Use the information given to find the scale factor of the
figure on the left to the figure on the right.
Problem 5 :
Solution :
Surface area of large shape : Surface area of small shape
= 36 : 25
k^{2} = 36/25
k = √36/25
k = 6/5
So, the scale factor is 6 : 5.
Problem 6 :
Solution :
Surface area of small shape : Surface area of large shape
= 7π : 175π
k^{2} = 7π/175π
k^{2} = 1/25
k = √1/25
k = 1/5
So, the scale factor is 1 : 5.
Problem 7 :
Solution :
Volume of small shape : Volume of large shape
10240 : 20000
k^{3} = 10240/20000
k^{3} = 64/125
k = ∛(64/125)
k = 4/5
So, the scale factor is 4 : 5.
Problem 8 :
Solution :
Volume of large shape : Volume of small shape
= 3240 : 120
k^{3} = 3240/120
k^{3} = 27
k = ∛27
k = 3
So, the scale factor is 3 : 1.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM