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

To solve this problem, we need to calculate the surface area of the rectangular solid. Here are the steps in detail:

Understand the problem:

The solid has a square base, with each side of the square base measuring 4 meters.
The volume of the solid is 112 cubic meters.
We need to find the surface area of the solid.
Step 1: Calculate the height of the solid:

The volume of a rectangular solid is given by: Volume = Base Area × Height
The base is a square with side length 4 meters. So, the base area is: Base Area = Side × Side = 4 × 4 = 16 square meters
Using the formula for volume: Volume = Base Area × Height 112 = 16 × Height Height = 112 ÷ 16 = 7 meters
Step 2: Calculate the surface area:

The surface area of a rectangular solid consists of:
Two square bases (top and bottom),
Four rectangular vertical faces.
Surface area formula: Surface Area = 2 × Base Area + Perimeter of Base × Height
The perimeter of the base (square) is: Perimeter = 4 × Side = 4 × 4 = 16 meters
Now, substitute the values: Surface Area = 2 × Base Area + Perimeter × Height Surface Area = 2 × 16 + 16 × 7 Surface Area = 32 + 112 Surface Area = 144 square meters
Final Answer: The surface area of the rectangular solid is 144 square meters.

Correct option: (a) 144 sq m