Answer:
V₂ = 810 cm³
Step-by-step explanation:
Given data : a₁ = 2 cm, V₁ = 30 cm³ and a₂ = 6 cm, V₂ = ?
If two prisms are similar then their corresponding sides are proportional.
First way:
Since we know the volume of the smaller prism and the volume of the larger is required and we know that the volume is calculated using the following formula:
V = a · b · c (cm³)
Accordingly, we will make following proportion:
2³ : 6³ = 30 : V₂ => 8 : 216 = 30 : V₂ => 8 · V₂ = 216 · 30 =>
V₂ = 6480/8 = 810 cm³
V₂ = 810 cm³
Second way:
We will assume that the sides of the first smaller prism are the following:
a₁ = 2cm, b₁= 5cm and c₁ = 3cm
V₁ = a₁ · b₁ · c₁ = 2 · 5 · 3 = 30 cm³ which is given value.
Accordingly, we will make following proportion:
a₂ : a₁ = b₂ : b₁ = c₂ : c₁ => 6 : 2 = b₂ : 5 = c₂ : 3 => 6/2 = b₂/5 = c₂/3 = 3 =>
b₂/5 = 3 and c₂/3 = 3 => b₂ = 5 · 3 = 15 cm and c₂ = 3 · 3 = 9 cm
Finally we get
V₂ = a₂ · b₂ · c₂ = 6 · 15 · 9= 810 cm³
V₂ = 810 cm³
God with you!!!
