Question

If the area of the square and circle is 1406.25 cm² and 1386 cm², respectively. Then, how many tiles whose length and breadth are 66 cm and 20 cm, respectively will be need fit in a rectangle region whose length is equal to the perimeter of the circle and the breadth is equal to the perimeter of the square?

1. 21
2. 15
3. 12
4. 14
5. 20

Answer 1

Correct Answer - Option 2 : 15

Given:

Area of square = 1406.25 cm²

Area of circle = 1386 cm²

Length of tile = 66 cm

Breadth of tile = 20 cm

Formula Used:

Area of the square = side × side

Area of circle = πr²

Area of rectangle = length × breadth

Calculation:

Area of square = 1406.25

⇒ Side of square = √(1406.25)

⇒ Side of square = 37.5 cm

Perimeter of square = 37.5 × 4

⇒ 150 cm

Area of circle = 1386

⇒ πr² = 1386

⇒ 22/7 × r² = 1386

⇒ r² = 441

⇒ r = 21 cm

Perimeter of circle = 2 × 22/7 × 21

⇒ 132 cm

Length of rectangle region = 132 cm

Breadth of rectangle region = 150 cm

Area of rectangle region = 132 cm × 150 cm

Are of one tile = 66 cm × 20 cm

Suppose n tiles will need to fit in the rectangle region.

⇒ 66 cm × 20 cm × n = 132 cm × 150 cm

⇒ n = (132 × 150)/(66 × 20)

⇒ n = 15