Question

The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to roll once over the play ground to level. Find the area of the play ground in square metres

Answer 1

Given :

• Diameter of a roller = 84 cm
• Thus , Radius$\sf=\dfrac{84}{2}=42cm$
• and Height = length = 120 cm
• And roller takes 500 complete revolutions to roll once over the play ground to level.

To find :

Area of the play ground in sq units .

Solution :

Area of the roller

$\sf=2\pi\:r\:h$

$\sf=2\times\dfrac{22}{7}\times42\times120$

$\sf=44\times6\times120$

$\sf=44\times720$

$\sf=31680cm^{-2}$

$\setlength{\unitlength}{1cm}\begin{picture}(12,4)\thicklines\put(2.7,2.7){ . }\put(6,3){\circle{2}}\put(6,6){\circle{2}}\put(6,3){\line(0,1){3}}\put(5.3,3){\line(0,1){3}}\put(6.73,3){\line(0,1){3}}\put(6,3){\line(1,0){0.7}}\put(6,6){\line(1,0){0.7}}\put(6.2,6.13){ r }\put(6.8,4.5){ h }\end{picture}$

Area of the playground

=area of 500 revolutions

=500×31680 cm²

=500×( 31680)/(100×100)m²

=15840m ²

Therefore, Area of the play ground is 15840 m²

Answer 2

given, the diameter of the roller =84cm=0.84m
then radius (r)=d/2=0.84/2=0.42
also given the length of the roller(h)=120cm=1.2m
we know that roller is in the shape of a cylinder
so csa of cylinder is the area covered in a single roll
so csa of cylinder=2πrh
=>2*22/7*42/10*12/10
=>2*22*0.6*1.2
=>31.68
also given that area of play ground is the area covered in 500rolls of the roller
so area of ground = 31.68*500
= 15840m square