Question

A circular ring of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5. The small side of the rectangle is

1. 80 cm
2. 30 cm
3. 120 cm
4. 60 cm

Answer 1

Correct Answer - Option 4 : 60 cm

Concept:

Circumference of a circle is given by

S = 2πr

Where r is the radius of a circle

Circumference of a rectangle is given by

P = 2(l + b)

Where l is the length ang b is width of a rectangle

Here A circular ring is cut and bent into the form of a rectangle so perimeter of circle and rectangle are same.

S = 2πr = P = 2(l + b)

2πr = 2(l + b)

Calculation:

Given:

radius r = 42 cm, l : b = 6 : 5

Let l = 6x ,b = 5x

2πr = 2(l + b)

2 π × 42 = 2(6x + 5x)

2 × 22/7 × 42 = 2(11x)

x = 12

So l = 6 × 12 = 72

b = 5 × 12 = 60

The small side of the rectangle is 60 cm.