Question

The diagonal of cube is 9 root 3 cm long . Find it's total surface

Answer 1

Given Question :-

• The diagonal of cube is 9 root 3 cm long . Find it's total surface.

ANSWER

Given that

• Diagonal of a cube = 9 √(3) cm

• Let egde of the cube be 'x' cm

We know that

• Diagonal of a cube is given by

$\blue{\bf :\implies\:Diagonal = \sqrt{3} \times edge}$

$\rm :\implies\:9 \sqrt{3} = x \sqrt{3}$

$\rm :\implies\:x \: = \: 9 \: cm$

Now,

• Surface Area of cube is given by

$\red{\bf :\implies\:Surface \: Area \: = \: {6x}^{2} }$

$\rm :\implies\:Surface \: Area \: = 6 \times {9}^{2}$

$\rm :\implies\:Surface \: Area \: = 6 \times 81$

$\rm :\implies\:Surface \: Area \: = \: 486 \: {cm}^{2}$

Additional Information

Cube: 

• A cube is a three-dimensional shape which is defined XYZ plane. It has six faces, eight vertices and twelve edges. All the faces of the cube are in square shape and have equal dimensions.

Cuboid: 

• A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.

Formula's of Cube :-

Total Surface Area = 6(side)²

Curved Surface Area = 4(side)²

Volume of Cube = (side)³

Diagonal of a cube = √3(side)

Perimeter of cube = 12 x side

Formula's of Cuboid

Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)

Curved Surface area = 2 height(length + breadth)

Volume of the cuboid = (length × breadth × height)

lDiagonal of the cuboid =√(l² + b² + h²)

Perimeter of cuboid = 4 (length + breadth + height)