Question

The diameter of a roller is 84 cm and it's length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of playground in m².

Answer 1

we are given

diameter=84cm

so,

radius =r=42cm

height=h=120cm

we know that

shape of roller is always in cylinder form

now, we can find surface area of cylinder

`SA=2\pi r h`

now, we can plug values

`SA=2\pi *42*120`

`SA=31667.25395 cm^2`

we know that

In one rotation , it covers area is 31667.25395 cm^2

There are 500 rotation

so, total area =
`500*31667.25395 cm^2`

total area =
`15833626.975 cm^2`

now, we need to change that area into m^2

we know that

`1cm^2=(1)/(10000) m^2`

now, we can multiply both sides 15833626.975

we get

`15833626.975cm^2=15833626.975*(1)/(10000) m^2`

`15833626.975cm^2=1583.36270 m^2`

so,

Area of playground is
`1583.36270 m^2`.............Answer