Question

If the diameter of the bigger circle is 26 cm and of the smaller circle, 112 cm, find (1) the difference of their circumferences and (2) the difference of their areas.

Answer 1

Diameter of the bigger circle = 126 cm
Radius = $\frac{d}{2}$ = 63 cm
Diameter of the smaller circle = 112 cm
Radius = $\frac{d}{2}$ = 56 cm
Circumference = πd = $\frac{22}{7}$ × 126 cm
⇒ Circumference = 396 cm
Circumference = πd = $\frac{22}{7}$ × 112 cm
⇒ Circumference = 352 cm
Difference between the circumferences of the circles = 396 cm − 352 cm = 44 cm
Area = πr²
Area of the bigger circle = π × 63² = $\frac{22}{7}\times 63\times 63$ = 12474 cm²
Area of the smaller circle = π × 56² = $\frac{22}{7}\times 56\times 56$ = 9856 cm²
Difference between the areas of the circles = 12474 cm² − 9856 cm² = 2618 cm²