Question

if the total surface area of a cube is 2400 CM square then find its lateral surface area ​

Answer 1

Answer:

Given :- TSA of cube=2400cm²

To find:-

LSA=?

First we have the calculate the edge 0f cube(a)

TSA=6a²

2400=6(a)²

a² = 2400/ 6

400=a²

a=20cm

LSA=4a²

=4(20)²

=4(400)

=4×400

= 1600 cm2

Answer 2

Given :-

Total surface area of a cube = 2400 cm

To Find :-

The lateral surface area ​of cube.

Solution :-

We know that,

• TSA = Total Surface Area
• LSA = Lateral Surface Area
• a = Side

Given that, TSA = 2400 cm

Let the side be 'a'.

Calculating the edge of cube,

$\underline{\boxed{\sf Total \ surface \ area=6a^{2}}}$

Substituting their values,

$\sf 2400 = 6a^{2}$

$\sf a^{2}=\dfrac{2400}{6}$

$\sf a^{2}=400$

$\sf a=\sqrt{400}$

$\sf a=20$

Therefore, the side of the cube is 20 cm

Finding LSA,

$\underline{\boxed{\sf Lateral \ surface \ area=4a^{2}}}$

Substituting them,

$\sf =4(20)^{2}$

$= \sf 4 \times 400$

$\sf =1600$

Therefore, the lateral surface area ​of the cube is 1600 cm²