# CHECK IF THE GIVEN FIGURES ARE SIMILAR

If two figures are similar then:

• the figures are equiangular, and
• the corresponding sides are in proportion.

Surface area of similar figures :

If the corresponding sides of similar figures are in the ratio k, then :

Area of image = k2 x area of object.

Volume of similar figures :

If the corresponding sides of similar solids are in the ratio k, then:

Volume of image = k3 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 = 24k = 24/80k = 3/10 60k = 18k = 18/60k = 3/10 40k = 12k = 12/40k = 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 = 27k = 27/81k = 1/3 54k = 18k = 18/54k = 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

k2 = 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

k2 = 7π/175π

k2 = 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

k3 = 10240/20000

k3 = 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

k3 = 3240/120

k3 = 27

k = 27

k = 3

So, the scale factor is 3 : 1.

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