Question

Please solve this....
Que from: Pearson IIT Foundation Mathematics​

Answer 1

Question :

From a square metal sheet of side 5 cm, three circular plates of radii 1/2 cm, 1 cm and 1 ¹/₂ cm are cut. If the area of the remaining part is equal to the area of a circle, then the area of that circle (in cm²) is ____

Answer :

The required area of the circle is 14.01 cm²

Step-by-step explanation :

Given :

• Side of the square metal sheet = 5 cm
• Radii of three circular plates are 1/2 cm , 1 cm and 1 ¹/₂ cm

To find :

the area of the circle which is equal to the area of the remaining part

Formulae :

Area of the square = (side)²

Area of the circle = πr²

Solution :

First we'll find the area of the square metal sheet and then areas of the three circular plates which are cut. Then, subtracting the sum of the areas of cut circular plates from the area of the square metal sheet gives us the area of the remaining part.

 

Area of the square metal sheet :

side = 5 cm

➙ Area = (side)²

➙ Area = (5 cm)²

➙ Area = 25 cm²

∴ Area of the square metal sheet = 25 cm²

Area of the circular plate of radius 1/2 cm :

radius = 1/2 cm = 0.5 cm

➙ Area = πr²

➙ Area = π(0.5 cm)²

➙ Area = 0.25π cm²

➙ Area = (0.25) (3.14) cm²

➙ Area = 0.785 cm²

∴  Area of the circular plate of radius 1/2 cm = 0.785 cm²

Area of the circular plate of radius 1 cm :

radius = 1 cm

➙ Area = πr²

➙ Area = (3.14) (1 cm)²

➙ Area = 3.14 cm²

∴ Area of the circular plate of radius 1 cm = 3.14 cm²

Area of the circular plate of radius 1¹/₂ cm :

radius = 1¹/₂ cm = 3/2 cm = 1.5 cm

➙ Area = πr²

➙ Area = (3.14) (1.5 cm)²

➙ Area = (3.14) (2.25) cm²

➙ Area = 7.065 cm²

∴ Area of the circular plate of radius 1¹/₂ cm = 7.065 cm²

Sum of the areas of the cut circular plates :

Sum of the areas of the cut circular plates = Area of the circular plate of radius ¹/₂ cm + Area of the circular plate of radius 1 cm + Area of the circular plate of radius 1¹/₂ cm

➙ Sum of the areas of the cut circular plates = 0.785 cm² + 3.14 cm² + 7.065 cm²

➙ Sum of the areas of the cut circular plates = 10.99 cm²

Area of the remaining part :

Area of the remaining part = Area of the square metal sheet - Sum of the areas of the cut circular plates

➙ Area of the remaining part = 25 cm² - 10.99 cm²

➙ Area of the remaining part = 14.01 cm²

∵ Area of the remaining part is equal to the area of a circle, the area of the circle is 14.01 cm²