Question

The length of a cuboid is 12cm breadth and I height are equal in measurements and it volume is 492 the cuboid is cut into 2 cubes find the LSA of each cube

Answer 1

Correction Question : The length of a cuboid is 12cm, breadth and  height are equal in measurements and it volume is 432 cm³, the cuboid is cut into 2 cubes. Find the LSA of each cube.

Answer :

144 cm²

Step-by-step explanation:

Given that;

Length of cuboid = 12 cm

Volume of cuboid = 432 cm³

Find breadth and height of cuboid :

Let the measure of Breadth and height  be x respectively.

According to the question;

Volume of cuboid = 432 cm³

⇒ l * b * h = 432 cm³

⇒ 12 * x * x = 432

⇒ 12 x² = 432

⇒ x² = 432 / 12

⇒ x² = 36

⇒ x = √36

⇒ x = 6 cm

Breadth = 6 cm

Height = 6 cm

Find the each side of cube :

As it is given that the, cuboid is cut into two pieces.

Each side of cube = length of cuboid /2

⇒ Each side = 12 / 2

⇒ Each side = 6 cm

Find the LSA of cube :

We know that ;

LSA of cube = 4 ( side )²

                     = 4 ( 6 )²

                     = 4 * 36

                     = 144 cm²

Hence, the LSA of cube is 144 cm²

Answer 2

According To The Question

Length of cuboid = 12 cm

Volume of cuboid = 432 cm³

Breadth and height of cuboid :

Suppose the Breadth and height  be p

By the Information :

Volume of cuboid = 432 cm³

⇒ l × b × h = 432 cm³

⇒ 12 × p × p = 432

⇒ 12 p² = 432

⇒ p² = $\bf\huge\frac{432}{12}$

⇒ p² = 36

⇒ p = √36

⇒ p = 6 cm

Breadth = 6 cm

Height = 6 cm

Cuboid is cut into two pieces

Each side of cube = $\bf\huge\frac{length\:of\:cuboid}{2}$

⇒ Each side = $\bf\huge\frac{12}{2}$

⇒ Each side = 6 cm

Lateral Surface Area of cube :

LSA of cube = 4 (side)²

= 4(6)²

= 4 × 36

= 144 cm²