If the ratio of the sides of two similar prisms is 1:3 and the volume of the second prism is 81, what is the volume of the first prism?
A. 3
B. 27
C. 243
D. 2187
@TraciBonita
@mathstudent55
@mjosedavid
@happytales

Question

If the ratio of the sides of two similar prisms is 1:3 and the volume of the second prism is 81, what is the volume of the first prism?
	A.	3
	B.	27
	C.	243
	D.	2187
@TraciBonita 
@mathstudent55 
@mjosedavid 
@happytales

i<3mybaby · Answer

@johnweldon1993

mathstudent55 · Answer

This is something you need to know about similar solids:

If the ratio of the sides of two solids is $a:b$, 

then the ratio of the areas is $a^2:b^2$, 

and the ratio of the volumes is $a^3 : b^3$

mathstudent55 · Answer

The sides of your prisms are in the ratio $1 : 3$.
What is the ratio of their volumes?

i<3mybaby · Answer

@mathmale 
@mathmate

mathstudent55 · Answer

I have explained something you need to know to solve your problem. You ignore my question and ask other people for help. Do you want to learn how to solve this problem, or are you interested in just an answer?

i<3mybaby · Answer

Honestly I am sorry I don't get it I am trying I really am but I just I dont get it I dont understandit and IDK WHAT THE RATIO IS THATS WHAT ITS ASKING

mathstudent55 · Answer

Now you did the right thing. You answered. I'll try to explain.

mathstudent55 · Answer

A ratio is a comparison of two numbers by DIVIDING them.

mathstudent55 · Answer

For example, if I have 2 quarters and 1 nickel, I can say the ratio of number of quarters to nickels is 2 to 1. The ratio can also be written as 2:1 and 2/1.

i<3mybaby · Answer

Oh..

mathstudent55 · Answer

Ok. Let's see how this applies to your problem.
In your problem there are two prisms of different sizes.

mathstudent55 · Answer

The information you have is that the prisms are similar.
That means the shapes look the same only one is larger than the other.
The other piece of information you have is the ratio of the sides is 3:1.
That means every side of the first prism is 3 times larger than the corresponding side of the second prism.

mathstudent55 · Answer

The problem with this problem now is how to interpret the given information.
Does the ratio of sides mean a ratio of the areas of the sides (the faces), or does the ratio of the sides mean a ratio of the lengths of the edges?

mathstudent55 · Answer

I assume it's the second possibility.
The ratio given is the ratio of the lengths of the edges.

If the lengths of the edges is 1:3, then the ratio of the volumes is 1^3 : 3^3 
or a ratio of 1 : 27.

This means the volume of the first prism is 27 times smaller than the volume of the second prism.

81/27 = 3

The volume of the first prism is 3.