What is the volume of the cube if the diagonal is 1?
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
The diagonal of a cube is given as sqrt (3L^2), where L is the length of the side.
We know that the diagonal is 1.
=> 1 = sqrt (3L^2)
=> 1^2 = 3L^2
=> L^2 = 1/3
=> L = sqrt( 1/3)
The volume of a cube is L^3
=> [sqrt (1/3)]^3
=> (1/3) sqrt (1/3)
(The entire section contains 2 answers and 140 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- How do we calculate the surface area of a cube if we know the volume is 343?
- 2 Educator Answers
- The surface area of a cube is 600cm^2. What is the volume of the cube.
- 2 Educator Answers
- What is the surface area of the cube if the volume is 214 ?
- 2 Educator Answers
- The volume of a sphere is given by the formula `V=4/3pi r^3` ; if the volume of the sphere is...
- 1 Educator Answer
- If the sides of a cube are measured with an error of 2% use differentials to estimate the...
- 1 Educator Answer
A cube is a regular prism which has a square top, bottom and lateral surfaces with equal length, width and height.
If the side of the cube is x, then its diagonal d is given by:
d = x^2+x^2+x^2 = 3x^2.
So , if diagonal d= 1, then 1= 3x^2 => x= sqrt(1/3) is the side of the cube.
So the volume of the cube = x^3 = (sqrt(1/3)}^3 = (1/3^3/2)= 1/sqrt27 = 0.19245 cubic units.
Student Answers