Question

A house with a flat roof is rectangular in shape, 10 m wide, 13 m long and 5 m high. It is to be painted inside and outside, and on the ceiling, but not on the roof or floor. The total number of sq. m. to be painted is:
A.360
B.460
C.650
D.590
E.720

Answer 1

Hint: Here, we will find the lateral surface area of a cuboid by substituting the given dimensions in the formula. Then we will multiply the lateral surface area by 2. Adding the area of rectangular ceiling with the obtained lateral surface area will give us the required area to be painted.

Formula Used:
We will use the following formulas:
1.Lateral Surface Area of a cuboid \[ = 2h\left( {l + b} \right){{\rm{m}}^2}\]
2.Area of rectangular ceiling of a house \[ = \left( {l \times b} \right){{\rm{m}}^2}\]

Complete step-by-step answer:
Here, the given house is in cuboidal shape.
The area that needs to be painted is the combination of both area of ceiling and the lateral surface area.
Therefore, lateral surface area of the house and area of the ceiling \[ = 2h\left( {l + b} \right) + \left( {l \times b} \right){{\rm{m}}^2}\]
Now, we are required to paint the house inside and outside, and on the ceiling, but not on the roof or floor.
Hence, this means that we have to find twice the lateral surface area of the house and add the area of ceiling to find the required area to be painted.
The area needs to be painted \[ = 2\left[ {2h\left( {l + b} \right)} \right] + \left( {l \times b} \right){{\rm{m}}^2}\]…..\[\left( 1 \right)\]
Substituting \[l = 13\], \[b = 10\] and \[h = 5\] in the above equation, we get
Hence, substituting these values in \[\left( 1 \right)\]
\[ \Rightarrow \]The area needs to be painted \[ = 2 \times \left[ {2\left( 5 \right)\left( {13 + 10} \right)} \right] + \left( {13 \times 10} \right)\]
Multiplying the terms inside the bracket, we get
\[ \Rightarrow \]The area needs to be painted \[ = 2 \times \left[ {10 \times 23} \right] + 130\]
\[ \Rightarrow \]The area needs to be painted \[ = 2 \times \left( {230} \right) + 130\]
Again, multiplying 2 by 230, we get
\[ \Rightarrow \]The area needs to be painted \[ = 460 + 130 = 590\]
Hence, the total number of sq. m. to be painted is \[590{{\rm{m}}^2}\]
Therefore, option D is the correct answer.

Note: Here the shape of the house is not given but we will assume it to be a cuboid because the dimensions of the house are given as length, breadth and height. A cuboid is a three-dimensional shape whose sides are rectangular. In real life, rooms are usually in the shape of a cuboid but if in case all the 4 walls and the top and bottom of a room have the same length, breadth, and height, this would mean that it is cubical in shape as a cube has all the sides equal and square-shaped. Some other examples of cuboidal figures which we see in our day to day life are matchboxes, shoeboxes, books, etc. All of these have a length, breadth and height respectively.