Question

The surface area of a cube is 96 cm? What is the new surface area of the cube if the length of each edge of
the cube is doubled?​

Answer 1

• New surface area is 384 cm².

Step-by-step explanation:

Given:-

• Surface area of a cube is 96 cm².

To find:-

• New surface are of cube if edge is doubled.

Solution:-

We know,

Surface area of cube = 6 a²

Where, a is edge of cube

Put the values:

$\implies$ 96 = 6 a²

$\implies$ 96/6 = a²

$\implies$ 16 = a²

$\implies$ √16 = a

$\implies$ a = 4

Edge of cube is 4 cm.

• Double the edge of cube for finding new surface area.

So,

$\implies$ 4 × 2

$\implies$ 8

Edge is 8 cm.

Now,

Put edge in surface area formula:

$\implies$ 6 × (8)²

$\implies$ 6 × 64

$\implies$ 384

Therefore,

Surface area of of cube is 384 cm².

Answer 2

Answer:

Given :-

• TSA of cube = 96 cm
• Length is doubled

To Find :-

New TSA of cube

Solution :-

As we know that

$\huge \bf \: TSA = 6 {a}^{2}$

$\sf \pink{ \implies \: 96 = 6 {a}^{2} }$

$\sf \green { \implies \: \dfrac{96}{6} = {a}^{2} }$

$\sf \pink { \implies \: 16 = {a}^{2} }$

$\sf \green { \implies \: \sqrt{16} = a}$

$\sf \pink { \implies \: 4 = a}$

Hence :-

The edge of cube is 4 cm

Now,

Total length of edge doubled

$\sf \green { \implies \: 4 \times 2}$

$\sf \pink { \implies \: 8}$

Now

Let's find New TSA

$\sf \green { \implies \: TSA \: = 6 \times {8}^{2} }$

$\sf \pink { \implies \: TSA = 6 \times 64}$

$\huge \bf \: New \: TSA = 384$