Question

the diameter of a roller is 84cm and its length is 120 cm. It takes 500 complete revolutions to roll once over the playground to level. find the area of playground in m square.

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Answer 1

$\mathbb{ SOLUTION }$ :

Given :
Diameter of roller = 84 cm
length [ height (h) ] = 120 cm

Radius of the roller = $\frac{Diameter}{2}$
Radius (r) of roller = $\frac{84}{2}$ = 42cm

We know that,
Curved Surface Area (CSA) of cylinder (roller)
= 2πrh

= 2 × $\frac{22}{7}$ × 42 × 120

= 31680 cm²

Now,
CSA = 1 revolution

=> 31680 cm² = 1 revolution

According to the question,
the roller takes 500 complete revolutions to roll once over that playground.

So,
area of playground = 500 × 31680 = 15840000cm²

Area in m² = $\frac{15840000}{10000}$ m² = 1584 m²

$\boxed{ 1 {m}^{2} = 10000 {cm}^{2} }$

Hence,
the area of the playground is $\boxed{\boxed{ 1584 {m}^{2} }}$

Answer 2

Given: diameter , d= 84cm and its length , h= 120cm

Since a roller is in cylindrical shape.

Height (h) of cylindrical roller = Length of roller = 120 cm

Radius (r) of the circular end of roller =

CSA of roller = 2πrh

84 / 2 = 42

Lateral surface area = 2*Pie*r*h = 2*22/7*42cm*120cm = 31680cm2.

∴Area of field = 500 × CSA of roller

= (500 × 31680) cm2

= 15840000 cm2

= 1584 m2

Thus, area of the playground = 1584 m2

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