How to find the diagonal of a cube - ISEE Upper Level (grades 9-12) Quantitative Reasoning
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What is the length of the diagonal of a cube with a side length of 
? Round to the nearest hundreth.
What is the length of the diagonal of a cube with a side length of
It is easiest to think about diagonals like this by considering two points on a cube (if it were drawn in three dimensions). We could draw it like this:
(Note that not all points are drawn in on the cube.)
The two points we are looking at are:
and 
Solve this by using the distance formula. This is very easy since one point is all 
s. It is merely:
This is approximately 
.
It is easiest to think about diagonals like this by considering two points on a cube (if it were drawn in three dimensions). We could draw it like this:
(Note that not all points are drawn in on the cube.)
The two points we are looking at are:
Solve this by using the distance formula. This is very easy since one point is all
This is approximately
Compare your answer with the correct one above
What is the length of the diagonal of a cube with a side length of 
? Round to the nearest hundreth.
What is the length of the diagonal of a cube with a side length of
It is easiest to think about diagonals like this by considering two points on a cube (if it were drawn in three dimensions). We could draw it like this:
(Note that not all points are drawn in on the cube.)
The two points we are looking at are:
and 
Solve this by using the distance formula. This is very easy since one point is all 
s. It is merely:
This is approximately 
.
It is easiest to think about diagonals like this by considering two points on a cube (if it were drawn in three dimensions). We could draw it like this:
(Note that not all points are drawn in on the cube.)
The two points we are looking at are:
Solve this by using the distance formula. This is very easy since one point is all
This is approximately
Compare your answer with the correct one above
What is the length of the diagonal of a cube with a volume of 
? Round to the nearest hundredth.
What is the length of the diagonal of a cube with a volume of
First, you need to find the side length of this cube. We know that the volume is:
, where 
is the side length.
Therefore, based on our data, we can say:
Solving for 
by taking the cube-root of both sides, we get:
Now, it is easiest to think about diagonals like this by considering two points on a cube (if it were drawn in three dimensions). We could draw it like this:
(Note that not all points are drawn in on the cube.)
The two points we are looking at are:
and 
Solve this by using the distance formula. This is very easy since one point is all 
s. It is merely:
This is approximately 
.
First, you need to find the side length of this cube. We know that the volume is:
Therefore, based on our data, we can say:
Solving for
Now, it is easiest to think about diagonals like this by considering two points on a cube (if it were drawn in three dimensions). We could draw it like this:
(Note that not all points are drawn in on the cube.)
The two points we are looking at are:
Solve this by using the distance formula. This is very easy since one point is all
This is approximately
Compare your answer with the correct one above
What is the length of the diagonal of a cube with a surface area of 
? Round your answer to the nearest hundredth.
What is the length of the diagonal of a cube with a surface area of
First, you need to find the side length of this cube. We know that the surface area is defined by:
, where 
is the side length. (This is because the cube is 
sides of equal area).
Therefore, based on our data, we can say:
Take the square root of both sides and get:
Now, it is easiest to think about diagonals like this by considering two points on a cube (if it were drawn in three dimensions). We could draw it like this:
(Note that not all points are drawn in on the cube.)
The two points we are looking at are:
and 
Solve this by using the distance formula. This is very easy since one point is all 
s. It is merely:
This is approximately 
.
First, you need to find the side length of this cube. We know that the surface area is defined by:
Therefore, based on our data, we can say:
Take the square root of both sides and get:
Now, it is easiest to think about diagonals like this by considering two points on a cube (if it were drawn in three dimensions). We could draw it like this:
(Note that not all points are drawn in on the cube.)
The two points we are looking at are:
Solve this by using the distance formula. This is very easy since one point is all
This is approximately
Compare your answer with the correct one above