Question

the radii of two concentric circles are 5cm and 4cm the difference in their area is ____​

Answer 1

QUESTION-:

the radii of two concentric circles are 5cm and 4cm the difference in their area is ____​

EXPLANATION-:

Figure is below -:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(1.2,0)(1.121,1.121)(0,1.2)\qbezier(1.2,0)(1.121,-1.121)(0,-1.2)\qbezier(0,-1.2)(-1.121,-1.121)(-1.2,0)\qbezier(-1.2,0)(-1.121,1.121)(0,1.2)\put(-0,0){\vector(-1,0){2.3}}\put(0,0){\vector(0,1){1.2}}\put(-1.9,0.2){ \bf 5\;cm }\put(0.2,0.3){ \bf 4\;cm }\end{picture}$

So to find the difference in area we will find area of bigger one and then subtract it from the smaller one .

Area of bigger circle-:

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{\bf\; \blue{ Area_{(circle)}=\pi R^2}}}}}$

Where

→R=5 cm

Putting values in the formula-:

$\longrightarrow \bf\;Area=\pi (5)^2\\\\\longrightarrow \boxed{\bf\; Area=25\pi}$

Therefore ,the area of bigger circle is 25 π

Now finding the area of smaller circle-:

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{\bf\; \blue{ Area_{(circle)}=\pi r^2}}}}}$

Where

→r=4 cm

Putting values in the formula-:

$\longrightarrow \bf\;Area=\pi (4)^2\\\\\longrightarrow \boxed{\bf\;Area=16\pi}$

Now finding the difference-:

$\dashrightarrow \underline{\underline{\bf\;Diiference_{(in\;area)}=Area_{(bigger\;circle)}-Area_{(small\;circle)}}}$

Putting values -:

$\longmapsto \underline{\bf\;Diiference_{(in\;area)}=25\pi-16\pi}}\\\\\longmapsto \underline{\boxed{\bf\;Diiference_{(in\;area)}=9\pi}}$

Therefore-:

Difference in area=9π

NOTE-:

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