Question

volume of a cube is 27 cube cm .The total surface area of a cube whose sides are doubled at the above cube is ???​

Answer 1

Step-by-step explanation:

Let a be the side of the cube.

Then its total surface area will be S

1

=6a

2

.

Now if the sides are doubled then the length of new sides be 2a.

And the total surface area will be 6×(2a)

2

=4×6a

2

=4×S

1

.

So surface area will be four times the original surface area.

Answer 2

Given :

• Volume of a cube = 27 cm³.

To Find :

• The total surface area of a cube whose sides are doubled at the above.

Solution :

Using Formula : Volume of Cube = a³

$\longrightarrow$ 27 = a³

$\longrightarrow$ √(3 × 3 × 3) = a

$\longrightarrow$ 3 = a

• Hence, we got the side of the cube = 3 cm.

According to the question :

• The total surface area of a cube whose sides are doubled at the above.
• Side = 3 cm.

The side of the required cube will be :

$\longrightarrow$ 2 × 3 cm

$\longrightarrow$ 6 cm

Using Formula : TSA of Cube = 6a²

$\longrightarrow$ TSA of Cube = 6 × 6²

$\longrightarrow$ TSA of Cube = 6 × 6 × 6

$\longrightarrow$ TSA of Cube = 216

• Hence, the Total surface area of the required Cube = 216 cm².