Question 11 of 42beginner💡 UnderstandShort Answer2 marks

The ratio of the perimeters of two circles is 5:4. What is the ratio of their radii?

Correct Answer

5:4

Exercise: Exercise Set 6.1 | Q: 8 | (Page 13)
For More Understanding

Explanation

The textbook explains that the ratio of the circumference (perimeter) to the diameter of a circle is a constant (the C/D ratio). Since the diameter is twice the radius, the perimeter is directly proportional to the radius. Therefore, the ratio of the perimeters of two circles will be exactly the same as the ratio of their radii.

Solution Steps

  1. Step 1: From the context, the ratio of circumference (perimeter) to diameter is a constant for all circles. Since diameter D=2rD = 2r, the perimeter is directly proportional to the radius.

  2. Step 2: Let the perimeters of the two circles be C1C_1 and C2C_2, and their radii be r1r_1 and r2r_2. Because CC is proportional to rr, we have C1:C2=r1:r2C_1 : C_2 = r_1 : r_2.

  3. Step 3: Given C1:C2=5:4C_1 : C_2 = 5 : 4, it directly follows that r1:r2=5:4r_1 : r_2 = 5 : 4.

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