Question

Two concentric circles have radii of 21 cm and 14 cm respectively. The area between the two circles is

a)462 sq cm
b)762 sq cm
c)770 sq cm
d)780 sq cm​

Answer 1

Answer:

Explanation:

Given :

• Radius of outer circle (R) = 21 cm
• Radius of inner circle (r) = 14 cm

To Find :

• The area between the two concentric circles.

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(1.2,0)(1.121,1.121)(0,1.2)\qbezier(1.2,0)(1.121,-1.121)(0,-1.2)\qbezier(0,-1.2)(-1.121,-1.121)(-1.2,0)\qbezier(-1.2,0)(-1.121,1.121)(0,1.2)\put(-0,0){\vector(-1,0){2.3}}\put(0,0){\vector(0,1){1.2}}\put(-1.9,0.2){ \bf R = 21cm }\put(0.2,0.3){ \bf r = 14 cm }\end{picture}$

Solution :

The area between the two concentric circles = Area of outer circle - Area of inner circle

$\implies$ A = πR² - πr²

$\implies$ A = π(R² - r²)

$\implies$ A = 22/7 × (21² - 14²)

$\implies$ A = 22/7 × (441 - 196)

$\implies$ A = 22/7 × 245

$\implies$ A = 22 × 35

$\implies$ A = 770 cm²

Hence :

The area between the two concentric circles is 770 cm².

Answer 2

Answer:

Πr^2= 21×21^² = 1385.4

step-2 14^²Π = 615.7

area between circles = 1385.4 - 615.7

= 769.7 = 770