Question

Arrange the following circles in the ascending order of their circumferences.

Answer 1

We know:
$\text{Circumference of a circle}=\pi \times \text{Diameter}$

$\therefore$ Circumference of the circle whose diameter is 6 in
$=\pi \times 6$
$=\frac{22}{7}\times 6$
$=\frac{132}{7}\text{in}$

Circumference of the circle with diameter 15 in
$=\pi \times 15$
$=\frac{22}{7}\times 15$
$=\frac{330}{7}\text{in}$

We know:
Diameter of a circle = 2 $\times$ Radius

$\therefore$ Circumference of the circle with radius 4 in
$=\pi \times 2\times 4$
$=\frac{22}{7}\times 8$
$=\frac{176}{7}\text{in}$

Circumference of circle with radius 10 in
$=\pi \times 2\times 10$
$=\frac{22}{7}\times 20$
$=\frac{440}{7}\text{in}$

Hence, the ascending order of the circumferences of the circles:
Diameter 6 in < Radius 4 in < Diameter 15 in < Radius 10 in.