Q-1 A wooden bookshelf has external dimensions as follows: Height, depth, breadth (see figure). The thickness of the plank is everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is paise per and the rate of painting is paise per find the total expenses required for polishing and painting the surface of the bookshelf.

Solution:

Given

Height

Depth

Breadth

Plank Thickness

Rate of polishing is

Rate of painting is

First lets calculate the outer area to be polished.

Now the shelf is open from the front, therefore there is only one face with sides of height and length.

Hence, external surface area of the shelf =

Now front face has some area, due to the thickness of the planks.

The area inside the outer edge of front face is , the area inside the inner edge of front face = . Therefore the area of front face occupied due to think planks = Outside area – Inside area

Therefore, total area to be polished = Outer area + Wooden area on the front face

Since cost of polishing , therefore, cost of polishing area

Now let’s calculate the inner area to be painted.

Internal depth, breadth and height are calculated by subtracting the length so planks.

Inner breadth = Outer breadth – width of right plank – width of left plank = .

Similarly, External height = Outer height – width of top plank – width of bottom plank = .

Since the bookshelf is open from the front, therefore the inner depth = outer depth – width of plank on the back

Therefore the inner surface are (since there is no front face)

Now, cost of painting

Therefore, cost of painting

Thus, total expense required for polishing and painting

So, it would take for polishing and painting the surface of the bookshelf.