A circular path has to be constructed around a circular ground. If the

1.	A circular path has to be constructed around a circular ground. If the areas of the outer and inner circles are 1386 m2 and 616 m2 respectively, find the width and area of the path.
Answer» Area of the outer circle = 1386 m² πR² = 1386m² Area of the inner circle = 616 m² πr² = 616m² Area of the path = Area of outer circle – Area of the inner circle 1386 m² – 616 m² Area of the path = 770m² Also πR² = 1386 R² = \(\frac{1386\times7}{22}\) R² = 63 x 7 R² = 9 x 7 x 7 R² = 3² x 7² R = 3 x 7 Outer Radius R = 21 m Again πr² = 616 \(\frac{22}{7}\) x r² = 616 r² = 28 x 7 r² = 4 x 7 x 7 r² = 2² x 7² r = 2 x 7 Inner radius r = 14m Width of the path = Outer radius – Inner radius = 21 – 14 Width of the path = 7m

A circular path has to be constructed around a circular ground. If the areas of the outer and inner circles are 1386 m2 and 616 m2 respectively, find the width and area of the path.

Answer»

Area of the outer circle = 1386 m²

πR² = 1386m²

Area of the inner circle = 616 m²

πr² = 616m²

Area of the path = Area of outer circle – Area of the inner circle

1386 m² – 616 m²

Area of the path = 770m²

Also πR² = 1386

R² = \(\frac{1386\times7}{22}\)

R² = 63 x 7

R² = 9 x 7 x 7

R² = 3² x 7²

R = 3 x 7

Outer Radius R = 21 m

Again πr² = 616

\(\frac{22}{7}\) x r² = 616

r² = 28 x 7

r² = 4 x 7 x 7

r² = 2² x 7²

r = 2 x 7

Inner radius r = 14m

Width of the path = Outer radius – Inner radius

= 21 – 14

Width of the path = 7m