If the length of diagonal of a cube is 13√3 cm, find its surface area.
Answers
Answer:
C.S.A of a cube = 676 cm^2 T.S.A of a cube = 1014 cm^2
Step-by-step explanation: Length of a cube = 13(square root )3 cm
length of a cube= {13(square root )3}/(SQUARE root of 3)
length of a cube =13 cm
#C.S.A of a cube = 4(a)^2
=4(13)^2
=4(169)
=676 cm^2
#T.S.A of a cube = 6(a)^2
=6(13)^2
=6(169)
=1014 cm^2
The surface area of the cube is 1014 square centimeters.
Given:
The length of the diagonal of the cube is (a) = 13√3 cm.
To Find:
The Surface Area of the cube =?
Solution:
We know that the length of the side diagonal of a cube of side length 'l' cm is l√2 cm whereas the length of the body diagonal of the cube is l√3 cm.
Here, we have given the length of the body diagonal of the cube 13√3 cm.
i.e., l√3 = 13√3
∴ l = 13 cm.
Now, we have the formula to calculate the surface area of the cube;
The surface area of the cube = 6l²
∴ The Surface area of the cube = 6(13²)
∴ The Surface area of the cube = 6 × 169
∴ The Surface area of the cube = 1014 cm²
Thus, its surface area is 1014 square centimeters.
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