Question

What will be the cost of painting the four walls of a room with length, width and height \[5m,3m\] and \[8m\] respectively. The room has one door and one window.
I.Cost of painting per square meter is \[Rs.25\]
II.Area of the window is \[2.25\] square meter which is half of the area of the door.
III.Area of the room is \[15\] square meter.

Answer 1

Hint: In this question we have given the length breadth and height of a room hence we will apply the formula for lateral surface area of cuboid and then we will find out the area of door and the area which is to be painted and we will check which statements are used so that we could obtain the given result.

Complete step-by-step answer:
A cuboid is a convex polyhedron having six rectangular faces, eight vertices, and twelve edges defined in geometry. It's a three-dimensional shape with \[x,y\] and \[z\] axes. In mathematics, we can see rectangular cuboid, rectangle box, right rectangular prism, right cuboid, rectangular parallelepiped, and rectangular hexahedron as alternative shapes that are precisely the same as cuboid. A box-shaped item is referred to as a cuboid.

Now according to the question:
We have given that:
Length is \[5m\] , Breadth is \[3m\] and Height is \[8m\]
Hence the area of the lateral surface is given by \[2\left( lh+bh \right)\]
 \[\Rightarrow 2\left( 5\times 8+3\times 8 \right)\]
 \[\Rightarrow 2\left( 40+24 \right)\]
 \[\Rightarrow 2\left( 64 \right)\]
 \[\Rightarrow 128\] square meter.
From statement one and two cost is \[Rs.25\] per square meter
And area of window is \[2.25\] square meter
Hence the area of the door is \[2\times 2.25=4.5\] square meter.
The area which is to be painted is:
 \[\Rightarrow 128-2.25-4.5\]
 \[\Rightarrow 121.25\] square meter
Hence the cost of painting the four walls will be:
 \[\Rightarrow 25\times 125.25\]
 \[\Rightarrow Rs.3031.25\]
We do not require the area of the room which is given in the third statement hence statement three is redundant.

Note: Students must note that each face of a cuboid is a rectangle, with \[90\] degree angles at the corners or vertices. Furthermore, the opposite faces are always the same. A book, for example, is a cuboid. It features six surfaces, each of which has the same dimensions as the opposing pair.