Question

the total surface area of a cube is 5400cm²find the surface area of the vertical face of the cube​

Answer 1

Given :

• Total surface area of cube = 5400 cm²

To find :

• Surface area of the vertical face of the cube

Concept :

Firstly, calculate the side of the cube by using the formula of total surface area of cube. Then substitute the values in the formula of surface area of the vertical face of the cube, the resultant value will be the required answer.

➳ Formula of Total surface area of cube :-

• TSA of cube = 6a²

➳ Formula to calculate surface area of the vertical faces of the cube :-

• Surface area of vertical face of cube = 4a²

where,

• a stands for the side of the cube

Solution :

Side of the cube :-

→ TSA of cube = 6a²

→ 5400 = 6a²

Transpoing 6 to the left hand side.

→ 5400 ÷ 6 = a²

→ 900 = a²

Taking square root on both the sides.

→ √900 = a²

→ ± 30 = a

As we know that any side cannot be in negative. So, the negative sign will be rejected.

→ ± 30 Reject - ve = a

→ 30 = a

★ Side of the cube = 30 cm

Using formula,

★ Surface area of vertical face of cube = 4a²

Substituting the given values,

→ Surface area of vertical faces of cube = 4 × (30)²

→ Surface area of vertical faces of cube = 4 × 900

→ Surface area of vertical faces of cube = 3600

Therefore,

• The surface area of the vertical face of the cube = 3600 cm²

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KNOW MORE :

• Volume of cube = side³
• Perimeter of cube = 12 × side
• Total surface Area of cuboid = 2(lb + bh + hl)
• Volume of cuboid =  length × breadth × height
• Perimeter of cuboid = 4 (l + b + h)

where,

• l stands for length
• b stands for breadth
• h stands for height