Question

If the length of a diagonal of a cube is 12 root 3 cm find its surface area and volume

Answer 1

Diagonal = s root 3 where s= side

Therefore side = 12cm

Surface Area = 6s^2 = 6(12)^2 = 6(144) = 864 cm^2

Volume = s^3 = 12^3 = 1728 cm^3

Please mark brainliest or thanks if it helped :D

Answer 2

Surface area of the cube is 864 cm² and volume is 1728 cm³ If the length of a diagonal of a cube is 12√3 cm

Given:

• Length of diagonal of a cube is 12√3  cm

To Find:

• Surface Area of the cube
• Volume of the cube

Solution:

• Cube has all its side length equal
• Volume of cube is given by  (side)³
• Surface area of cube is given by  6(side)²
• Diagonal of cube is given  side√3

Step 1:

Assume that Side length of the cube is  x cm

Step 2:

Find diagonal of the cube and equate with 12√3

√(x² + x² + x²)  = 12√3

=> √(3x²)  = 12√3

=> x√3 = 12√3

=> x = 12

Step 3:

Find Surface area by substituting x= 12 in 6x²

Surface area = 6x²

Surface area = 6(12)²

Surface area = 864 cm²

Step 4:

Find volume by substituting x= 12 in  x³

Volume =  x³

Volume =  (12)³

volume = 1728 cm³

Surface area of the cube is 864 cm² and volume is 1728 cm³