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Procedure - Area of the Circle is half the product of its Circumference & Radius, Class 9 Math | Extra Documents & Tests for Class 9 PDF Download

As performed in real lab:

Materials required:

Coloured paper, compass, scale, a pair of scissors, gum, colours

Procedure:

  • Draw a circle of radius r = 4 cm (say) on the paper.

  • Divide the circle into 16 equal parts. [Fig (a)]

  • Cut all the 16 parts and arrange them to get the [Fig (b)].

  • Take any part from any side and further divide it into 2 parts. [Fig (c)]

  • To complete the shape of rectangle arrange these two smaller parts at the corners of the shape obtained in [Fig (b)].

  • Find the length and the breadth of the rectangle so formed [Fig (d)].

  • Find the area of the rectangle.

 

Procedure - Area of the Circle is half the product of its Circumference & Radius, Class 9 Math | Extra Documents & Tests for Class 9

Procedure - Area of the Circle is half the product of its Circumference & Radius, Class 9 Math | Extra Documents & Tests for Class 9
          Fig (b)


Procedure - Area of the Circle is half the product of its Circumference & Radius, Class 9 Math | Extra Documents & Tests for Class 9

Procedure - Area of the Circle is half the product of its Circumference & Radius, Class 9 Math | Extra Documents & Tests for Class 9
         Fig (d)

As performed in Simulator:

  • Click on scale (between 2 and 3) in workbench to draw circle.

  • Click on the circle to mark 16 sectorials parts & color them differently.

  • Move mouse over each wedge to align them in a row.

  • Click on next button below to color wedges & divide in two group.

  • Click blue group to rotate and align.

  • Drag the blue group and drop over green group to join and form parallelogram.

  • Click on left most wedge to cut it into two parts.

  • Drag the red part and attach to the right end so as to form a rectangle.

  • This is a rectangle whose area can be calculated as (Length x Breadth).

Observations:

  • The students will observe that the area of rectangle   Procedure - Area of the Circle is half the product of its Circumference & Radius, Class 9 Math | Extra Documents & Tests for Class 9
  • The students will observe that the rectangle is obtained from parts of circle. Hence area of circle = π x r2

The document Procedure - Area of the Circle is half the product of its Circumference & Radius, Class 9 Math | Extra Documents & Tests for Class 9 is a part of the Class 9 Course Extra Documents & Tests for Class 9.
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FAQs on Procedure - Area of the Circle is half the product of its Circumference & Radius, Class 9 Math - Extra Documents & Tests for Class 9

1. What is the formula for finding the area of a circle?
Ans. The formula for finding the area of a circle is given by A = πr², where A represents the area and r represents the radius of the circle.
2. How can the area of a circle be half the product of its circumference and radius?
Ans. The statement that the area of a circle is half the product of its circumference and radius is not true. In fact, the area of a circle is given by a different formula (A = πr²) and is not directly related to the circumference and radius in this way.
3. Is there a relationship between the area, circumference, and radius of a circle?
Ans. Yes, there is a relationship between the area, circumference, and radius of a circle. The circumference of a circle can be calculated using the formula C = 2πr, where C represents the circumference and r represents the radius. The area of a circle, as mentioned earlier, can be calculated using the formula A = πr². However, the area and circumference are not directly dependent on each other.
4. How can I find the area of a circle if I know its circumference?
Ans. To find the area of a circle if you know its circumference, you can use the formula A = (C²)/(4π), where A represents the area and C represents the circumference. This formula can be derived using the relationship between the circumference and radius of a circle.
5. Are there any other formulas to find the area of a circle?
Ans. Apart from the formula A = πr², there is another formula to find the area of a circle using its diameter. The formula is A = (πd²)/4, where A represents the area and d represents the diameter of the circle. This formula can be derived by substituting the value of the radius (r = d/2) in the original formula A = πr².
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