Question

Find the surface area of a cuboid with dimensions \[4\times 2.5\times 2\] (in inches)
(a) \[46\,i{{n}^{2}}\]
(b) \[12\,i{{n}^{2}}\]
(c) \[26\,i{{n}^{2}}\]
(d) \[14\,i{{n}^{2}}\]

Answer 1

Hint: General notation of dimensions of cuboid is \[l\times b\times h\]. Total surface area of a cuboid is the sum of the areas of all its 6 rectangular faces that is \[\text{A=}2(lb+bh+lh)\].

Complete step-by-step answer:
Before proceeding with the question we should understand the definition of cuboid.
A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel and equal in dimensions. But not all the faces of a cuboid are equal in dimensions. A cuboid is a closed 3-dimensional geometrical figure bounded by six rectangular plane regions.

Total surface area of a cuboid is sum of the areas of all its 6 rectangular faces.
\[\text{A=}2(lb+bh+lh).......(1)\] where l is length, b is breadth and h is height
General notation of dimensions of cuboid is \[l\times b\times h\]. So from the information mentioned in the question, length is 4 inch, breadth is 2.5 inch and height is 2 inch.
So from equation (1) we get the surface area of a cuboid as,
\[\text{A=}2(4\times 2.5+2.5\times 2+4\times 2).......(2)\]
Now simplifying equation (2) by first multiplying each terms we get,
 \[\text{A=}2(10+5+8).......(3)\]
Adding all the terms in equation (3) and multiplying it by 2 we get,
\[\text{A=}2\times 23=46\,i{{n}^{2}}\]
Hence the surface area of a cuboid is \[46\,i{{n}^{2}}\]. So the correct answer is option (a).
Note: Here in this type of questions we have to keep in my mind the general notation of the dimensions of a cuboid. Also we have to remember the formula of the total surface area of the cuboid to solve this problem. Here when we write the final answer we have to mention the unit or else marks will get deducted by the invigilator.