What is the length of a diagonal of a cube with a side length of 10 cm? 200 cm 210cm 300 cm 320cm
2 answers:
Answer:
The length of the diagonal of the cube = √(3 × 10²) = √300 cm
Step-by-step explanation:
* Lets revise the properties of the cube
- It has six equal faces all of them are squares
- It has 12 vertices
- The diagonal of the cube is the line joining two vertices in opposite
faces (look to the attached figure)
- To find the length of the diagonal do that:
# Find the diagonal of the base using Pythagoras theorem
∵ The length of the side of the cube is L
∵ The base is a square
∴ The length of the diagonal d = √(L² + L²) = √(2L²)
- Now use the diagonal of the base and a side of a side face to find the
diagonal of the cube by Pythagoras theorem
∵ d = √(2L²)
∵ The length of the side of the square = L
∴ The length of the diagonal of the cube = √[d² + L²]
∵ d² = [√(2L²)]² = 2L² ⇒ power 2 canceled the square root
∴ The length of the diagonal of the cube = √[2L² + L²] = √(3L²)
* Now lets solve the problem
∵ The length of the side of the square = 10 cm
∴ The length of the diagonal of the cube = √(3 × 10²) = √300 cm
- Note: you can find the length of the diagonal of any cube using
this rule Diagonal = √(3L²)
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The diameter AC = 0.35 meter.
We have to find the side of square.
Let the measure of side of a square be 'l' meter
In triangle ABC,
By Pythagoras theorem, we get
So, l = 0.25 meter
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Answer:
There are 524,560 ways that the committee can be appointed.
Step-by-step explanation:
There are 9 different positions, a president, 3 officers and five committee members.
So
P - O1 - O2 - O3 - C1 - C2 - C3 - C4 - C5
There are 17 candidates, any of them can be president. So P = 17.
All of the others can be an officers. So O1 = 16, O2 = 15(17 subtracted by the president and O1), O3 = 14.
The officers can be committee members, so, C1 = 16, C2 = 15, C3 = 14, C4 = 13, C5 = 12.
How many different ways can the committee be appointed?
This is the sequence C1...C5:
There are 524,560 ways that the committee can be appointed.