Question

Ram Gopal has a circular shaped plot of radius 50 cm he wants to construct a building and met a civil engineer miss Kalpana she prepared two types of plan in plan length of 80cm breadth of 60 cm is a rectangular shaped building and in Plan B is a square shaped building ramgopal wants to use maximum area of land for construction which plant did he choose which construction covers more area and by how much?

Answer 1

Ram Gopal had chosen the plan B of square-shaped building.

Plan B of the square-shaped building covers more area by 200 cm².

Step-by-step explanation:

Step 1:

The radius of the circular shaped plot, r = 50 cm

∴ The area of the circular shaped plot  is given by,

= πr²

= 3.14 × 50²

= 7850 cm² ...... (i)

Step 2:

For the Plan A of a rectangular shaped building:

Length, l = 80 cm

Breadth, b = 60 cm

∴ The area covered by the rectangular-shaped building  is given by,

= l × b

= 80 × 60

= 4800 cm² ...... (ii)

Step 3:

For the plan B of a square-shaped building plot:

We know that the diagonal of the square will be equal to the diameter of the circle , so,

Diagonal of the square, d = 2 * 50 = 100 cm

∴ The side of the square -shaped building will be,

= $\frac{d}{\sqrt{2}}$

= $\frac{100}{\sqrt{2}}$

multiplying and dividing by  $\sqrt{2}$

= 50√2 cm

∴ Area covered by the square-shaped building is,

= side²

= [50√2]²

= 5000 cm² ....... (iii)

Step 4:

Comparing (i), (ii) & (iii), we can conclude

Area of the plan B of the square building is more .

⇒ The plan B covers the maximum area of the land  for construction.

∴ Ram Gopal chooses the plan B of square building  

And,

The plan B covers more area by,

= 5000 - 4800

= 200 cm²

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