Question

perimeter of rectangle
28. How many times a wheel of radius 35cm must rotate to go 352cm? Also find the
area of the wheel​

Answer 1

SOLUTION

Radius of the wheel = 35cm.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 35\ cm}\end{picture}$

Total distance traveled by the wheel = 352cm.

$\boxed{\sf Number \: of\: rotation\: made\: by \: the \: wheel = \dfrac{Total \; distance \;covered}{Distance \: covered\: in \: one\: rotation} }$

Distance covered in one rotation = 2πr , Where r is the radius of the circle.

$\implies \sf Distance \: covered \;in \;one\; rotation = 2* \dfrac{22}{7} * 35$

$\implies \sf Distance \: covered \;in \;one\; rotation = 2* 22* 5$

$\implies \sf Distance \: covered \;in \;one\; rotation = 220cm.$

Therefore,

$\sf Number \: of\: rotation\: made\: by \: the \: wheel = \dfrac{352}{220}$

$\implies$ Number of rotation made by the wheel = 1.6.

AREA

Area of a circle = πr² , Where r is the radius of the circle.

Here,

r = 35cm.

$\implies \sf Area \: of \: the \: circle = \dfrac{22}{7}*(35)^2$

$\implies \sf Area \: of \: the \: circle = \dfrac{22}{7}*1225$

$\implies \sf Area \: of \: the \: circle = 22 * 175$

$\implies$ Area of the circle = 3850 cm².