In a cube each face will be square,
a^{2} + a^{2} = y^{2}
2a^{2} = y^{2}
y = √2a^{2}
y = a√2
Then,
a^{2} + y^{2 }= x^{2}
a^{2} + (a√2)^{2 }= x^{2}
a^{2} + a^{2}(2) = x^{2}
a^{2} + 2a^{2} = x^{2}
3a^{2 }= x^{2}
x = √3a^{2}
x = a√3
So, length of the diagonal of a cube is a√3.
Here a is side length.
Problem 1 :
Find the value of x.
Solution :
y^{2} = 5^{2} + 5^{2} y^{2} = 25 + 25 y^{2} = 50 y = √50 y = √(5 ⋅ 5 ⋅2) y = 5√2 |
5^{2} + y^{2} = x^{2} 5^{2} + 50 = x^{2} 25 + 50 = x^{2} x^{2} = 75 x = √75 x = √(5 ⋅ 5 ⋅3) x = 5√3 |
Problem 2 :
Find the lateral surface area of a cube, if its diagonal is √6 cm.
Solution :
Given, diagonal of the cube = √6 cm
Diagonal of the cube = √3 a
√3 a = √6
a = √6/√3
a = √2 cm
Lateral surface area of cube = 4a²
= 4 × (√2)²
= 4 × 2
= 8 cm²
Problem 3 :
The side length of a cube is 5 meters. What is the length of its diagonal across one of the faces?
Solution :
Side length of cube (a) = 5 m
Length of the diagonal of a cube = a√3
length of the diagonal = 5√3
Problem 4 :
Find the length of the face diagonal of a cube when the side measures 9 units. Use the diagonal face formula of a cube.
Solution :
Length of one face diagonal of cube = a√2
Side length of the cube = 9 units
length of one face of diagonal = 9√2
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM