the diagonal of one side of a cube is 11.3 cm to 3 s.f . Find the cubes volume
Answers
Answer:
TESTS HOME
SIGN IN
Create an Account to Track Your Scores
Vt logo b color
Intermediate Geometry : How to find the diagonal of a cube
Study concepts, example questions & explanations for Intermediate Geometry
Example Questions
Intermediate Geometry Help » Solid Geometry » Cubes » How to find the diagonal of a cube
Find The Diagonal Of A Cube : Example Question #1
Find the diagonal of a cube with a side length of 1 .
Possible Answers:
diagonal=6–√
diagonal=22–√
diagonal=3–√
diagonal=2–√
diagonal=23–√
Correct answer:
diagonal=3–√
Explanation:
The diagonal of a cube is simply given by:
diagonal=x⋅3–√
Where x is the side length of the cube.
So since our x=1
diagonal=1⋅3–√
diagonal=3–√
Report an Error
Find The Diagonal Of A Cube : Example Question #2
If the volume of a cube was one eighth, what is the diagonal of the cube?
Possible Answers:
3–√2
23–√3
32−−√
12
18
Correct answer:
3–√2
Explanation:
Write the volume of a cube and substitute the given volume to find a side length.
V=s3
18=s3
s=12
Write the diagonal formula for a cube and substitute the side length.
d=s3–√=3–√2
Report an Error
Find The Diagonal Of A Cube : Example Question #3
Find the length of a diagonal of a cube with volume of 64in.3
Possible Answers:
83–√in.
42–√in.
8in.
16in.
43–√in.
Correct answer:
43–√in.
Explanation:
There is a formula for the length of a cube's diagonal given the side length. However, we might not remember that formula as it is less common. However, we can also find the length using the Pythagorean Theorem.
But first, we need to find the side length. We know the volume is 64. Our formula for volume is
V=s3
Substituting gives
64=s3
Taking the cube root gives us a side length of 4. Now let's look at our cube.
9
We need to begin by finding the length of the diagonal of the bottom face of our cube (the green segment). This can be done either by using the Pythagorean Theorem or by realizing that the right triangle is in fact a 45-45-90 triangle. Either way, we realize that our diagonal (the hypotenuse) is 42–√.
10
We now seek to find the diagonal of the cube (the blue segment). We do this by looking at the right triangle formed by it, the left vertical edge, and the face diagonal we just found. This time our only recourse is to do the Pythagorean Theorem.
42+(42–√)2=d2
16+32=d2
48=d2
d=43–√
In general, the formula for the diagonal of a cube with side length s is
d=s3–√