Question

Prism A is similar to Prism B. The volume of Prism A is 4320 cm3.

What is the volume of Prism B?

A.) 34,560 cm3

B.) 2160 cm3

C.) 1080 cm3

D.) 540 cm3

Answer 1

Since Prism A is similar to Prism B, the ratio of their volumes is the same as the ratio of their corresponding side lengths cubed. By using this ratio and the given volume of Prism A, we can determine the volume of Prism B.

Step-by-step explanation:

Since Prism A is similar to Prism B, we can say that the ratio of their volumes is the same as the ratio of their corresponding side lengths cubed.

Let VA be the volume of Prism A and VB be the volume of Prism B. Since VA = 4320 cm³, we can set up the equation:

VA : VB = (sA)³ : (sB)³

where sA is the side length of Prism A and sB is the side length of Prism B.

By substituting the values, we get:

4320 : VB = (sA)³ : (sB)³

4320 : VB = (sA)³/(sB)³

Since the prisms are similar, the ratio of their side lengths is the same, so we can simplify to:

4320 : VB = 1³ : s³

By cross-multiplying, we get:

4320 × s³ = VB

Simplifying further, we have:

VB = 4320 × s³

Therefore, the volume of Prism B is 4320 times the volume of Prism A.

Answer 2

Alright, lets get started.

Prism A and prism B are similar to each other.

Suppose the dimensions of prism A are : l, w, h

So, the volume of prism A =
`l*w*h`

The dimensions of prism B are half of prism A.

Means , the dimensions of prism B will be :
`(l)/(2) , (w)/(2) , (h)/(2)`

So, volume of prism B =
`(l)/(2)* (w)/(2) *(h)/(2)`

So, volume of prism B =
`(1)/(8) * (l*w*h)`

volume of prism B =
`(1)/(8) *` volume of prism A

volume of prism B =
`(1)/(8) * 4320`

volume of prism B
`= 540 cm^(3)` : Answer option D

Hope it will help :)