Question

A rectangular solid has a square base, with each side of the base measuring 4 metres. If the volume of the solid is 112 cubic meters, what is the surface area of the solid?
(a) 144 sq m
(b) 250 sq m
(c) 172 sq m
(d) 228 sq m

Answer 1

Hint: First of all, we will draw a figure to understand the question better. The volume of the solid is given. The volume of the rectangular solid is given by the relation V = lbh, where V is the volume, l is the length, b is the breadth and h is the height. It is given that the base is square in shape. This means, the length and the base of the base is equal. From the formula for volume, we can find the height. Once, we find the height, we can proceed to find the surface area. The total surface area of the solid will be the sum of all the faces. So, there are 2 bases and 4 vertical faces in a rectangular solid. Thus, we can find the total surface as 2(area of bases) + 4(area of face).

Complete step-by-step answer:
The required figure is as follows:

It is given that the volume of the rectangular solid is 112 cu m.
The base is square and has length and breadth both as 4.
The volume of a rectangular solid is given by V = lbh.
Thus, 112 = 4 $ \times $ 4 $ \times $ h
 $ \Rightarrow $ h = 7
Therefore, the height of the solid is 7 m.
Now, we will find the total surface area of the rectangular solid.
First, we will find the area of the base. The dimensions of the base are 4 $ \times $ 4.
Therefore, the area of the base = 16 sq m
The dimensions of a face are 4 $ \times $ 7.
Therefore, the area of a face = 28 sq m
Total surface area will = 2(area of base) + 4(area of face)
Surface area = 2(16) + 4(28)
Thus, the total surface area of the rectangular solid is 144 sq m.
So, the correct answer is “Option A”.

Note: The relation for the total surface area of a rectangular solid is given as 2(lb + bh + hl). Since, in our problem, the length and the breadth of the base is equal, this area modifies as 2 $ \left( {{\text{a}}^{2}} \right) $ + 4(ah), where a is the length of the side of the square base.