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- When two Triangles are Congruent?
- Ratio of Area and Volume for similar figures
- Examples
When two Triangles are Congruent?
When two Triangles are Congruent?
All corresponding sides are equal. (S S S)
a = p, b = q, c = r
Two sides and in-between angle are equal. (S A S)
a = p, <B = <Q, c = r
Two angles and in-between side are equal. (A S A)
<A = <P, b = q, <C = <R
Both have right angles, equal hypotenuse, equal side. (R H S)
Ratio of Area and Volume for similar figures
Ratio of Area and Volume for similar figures
Length = a : b = 2 : 3
Area = a² : b²
= 2² : 3² = 4 : 9
Volume = a³ : b³
= 2³ : 3³ = 8 : 27
Examples
Examples
Height of two similar cylinders are in the ratio 4 : 3.
Find ratios of their (a) surface areas (b) volumes.
Ratio of heights = 4 : 3
Ratio of surface areas = 42 : 32 = 16 : 9
Ratio of volumes = 43 : 33
= 64 : 27
Surface areas of two similar containers are in the ratio 9 : 25.
Find ratios of their (a) heights (b) volumes.
Ratio of surface areas = 9 : 25
Ratio of heights = Sqrt(9) : Sqrt(25) = 3 : 5
Ratio of volumes = 33 : 53 = 27 : 125
Question
Question
A model of a cylindrical water tank is in the scale of 1: 30 (a) If the actual height of the water tank is 3 m, find the height of the model in cm. (b) if the base area of the model is 20 cm2 , find the actual base area of the tank in m2 (c) if the model has a volume of 2000 cm3 , find the actual volume of the tank in m3
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