Question

What is the surface area of a television $20inches$ long, $15inches$ wide, and $5inches$ high?
A.$980i{n^2}$
B.$950i{n^2}$
C.$915i{n^2}$
D.$925i{n^2}$

Answer 1

Hint: As we know that the television is a three-dimensional object because it is present in a three-dimensional plane. It means we are given the dimensions of the cuboid (because dimensions are not the same). A parallelepiped (a solid formed by three pairs of parallel and congruent parallelograms) whose faces are rectangles and adjacent faces are perpendicular is called a cuboid. Here, we are given the length, breadth, and height of a cuboid. So we will put these values in the surface area formula of the cuboid to find our answer.
Formula:
Surface area of a cuboid = 2(length × breadth + breadth × height + height × length) sq. units
Or
Surface area of a cuboid = $2\left( {lb + bh + hl} \right)sq.{\text{ }}units$

Complete step-by-step answer:
We have,
Length of television = $20inches$
Breadth of television = $15inches$
Height of television = $5inches$.

As we know, Surface area of a cuboid = $2\left( {lb + bh + hl} \right)sq.{\text{ }}units$
Surface area of television = $2\left( {20inches \times 15inches + 15inches \times 5inches + 5inches \times 20inches} \right)$
It can also be written as,
Surface area of television = \[2\left( {20 \times 15 + 15 \times 5 + 5 \times 20} \right)inche{s^2}\]
On multiplying terms inside the bracket, we get
Surface area of television = \[2\left( {300 + 75 + 100} \right)inche{s^2}\]
Add the terms written in bracket
Surface area of television = \[2\left( {475} \right)inche{s^2}\]
On multiplying, we get
Surface area of television = \[950inche{s^2}\]
Therefore, the correct option is B.
So, the correct answer is “Option B”.

Note: As in the given question the dimensions of television are different so it means that it is a cuboid. But, if the dimensions were the same it would be a cube. We should be careful about the unit. The calculation should be done in the same unit. We should take care of the calculations so as to be sure of our final answer.