Question

Please, I am in desperate need of help. I'd also appreciate if you could explain to me how you got the answer. I dont quite understand how the teacher explained it. Thank you.

Answer 1

V₂ = 810 cm³

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!!!