### Solution:

Concept- We will use the formula given by which is known as the lateral surface area of the cuboid.Here I is the length of the cuboid, is the breadth and is the height of the cuboid.

We'll apply the equation provided by also known as the cuboid's lateral surface area.

We can answer theQuestion with the aid of this formula. I, b, and represent the cuboid's length, breadth, and height, respectively.

We'll first think about the word "lateral surface" in order to answer the question. The area of the top and the curved surface are actually included when calculating lateral surface. So, by taking into account the cuboid's surface and its area at the top, we may get the lateral surface area. Essentially, the square area provided by the side square determines the area of the cuboid's top.

However, in addition to the area of the square on top of the cuboid, we must also take into account the cuboid's surface if we need to determine the lateral surface area. This can be expressed mathematically as Below is a diagram that corresponds to the dimensions specified in the question.

The cuboid formula is changed into a new equation by substituting these values for the cuboid's specified length, breadth, and height, which are each symbolized by the letters l, b, and h. The cuboid's length is signified by letters l, 12 cm by b, and 7.5 cm by h. So, we obtain

area of cuboid area of cuboid area of cuboid area of cuboid area of cuboid Consequently, the cuboid has a 510 centimeter square surface area.

Hence, the correct answer is option 2.

Syllabus: CBSE