Find the following ratios.

(i) The ratio of radius to circumference of the circle.

(ii) The ratio of circumference of circle with radius r to its area.

(iii) The ratio of diagonal of a square to its side, if the length of side is 7 cm.

(iv) The lengths of sides of a rectangle are 5 cm and 3.5 cm. Find the ratio of its perimeter to area.

(i) Let r be the radius of a circle.

Circumference of circle = 2πr

Ratio of radius to circumference of circle = r/2πr

= 1/2π

= 1 : 2π

(ii) Let r be the radius of a circle.

Circumference of circle = 2πr

Area of the circle =2πr²

Ratio of radius to circumference of circle = 2πr/πr²

= 2/r

= 2 : r

(iii) Side of square = 7 cm

Diagonal of square = √2 × side = 7√2 cm

Ratio of diagonal of a square to its side = 7/7√2

= 1/√2

= 1 : √2

(iv) Length of rectangle = 5 cm

Breadth of rectangle = 3.5 cm

Perimeter of rectangle = 2(Length + Breadth)

= 2(5+3.5)

= 2(8.5)

= 17 cm

Area of rectangle = Length × Breadth

= 5 × 3.5

= 16.5 cm²

Ratio of Perimeter to area of rectangle

= 17/16.5

= 170/165

= 34/33