Question

An aquarium is in the form of a cuboid whose external measures are \[80cm30cm40cm.\] The base, side faces and back face are to be covered with a coloured paper. Find the area of paper needed?
A.\[3000c{m^2}\]
B.\[5000c{m^2}\]
C.\[8000c{m^2}\]
D.\[7000c{m^2}\]

Answer 1

Hint: Here, to find the area of paper needed we will calculate the area of different faces
\[\left( {i.e.{\text{ }}rectangle} \right)\]and add them.

Complete step by step solution:
We are given that:
The base, side faces and back face are to be covered with coloured paper.
So, except for the top and front face, all faces are to be covered with coloured paper. Thus,
\[\left( l \right){\text{ }}Length{\text{ }} = {\text{ }}80cm\]
\[\left( b \right){\text{ }}Breadth{\text{ }} = {\text{ }}30{\text{ }}cm\]
\[\left( h \right){\text{ }}Height{\text{ }} = {\text{ }}40{\text{ }}cm\]
So, area of paper needed \[ = {\text{ }}area{\text{ }}of{\text{ }}base{\text{ }} + {\text{ }}2\left( {area{\text{ }}of{\text{ }}side{\text{ }}face} \right){\text{ }} + {\text{ }}\left( {area{\text{ }}of{\text{ }}back{\text{ }}face} \right)\]
\[ = {\text{ }}(80 \times 30){\text{ }} + {\text{ }}2(30 \times 40){\text{ }} + {\text{ }}(80 \times 40)\]
\[ = {\text{ }}2400{\text{ }} + {\text{ }}2400{\text{ }} + {\text{ }}3200\]
$ = 8000c{m^2}$
$\therefore $Area of paper needed to cover the aquarium is \[8000c{m^2}\]
   So, Option D is correct.

Note: As we know area of rectangle \[ = {\text{ }}l*b\]
So, we have to be careful while finding the area of different faces as each face will have different dimensions.i.e.for backface we will calculate area using length and height, and for side faces we will use breadth and height and so on.