Question

The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2.
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Answer 1

Given:

• Diameter of Roller is 84 cm.
• Length of Roller is 120 cm.

To Find:

• Area of Playground in m².

Solution :

here , diameter = 84 cm

• Radius = 84/2 = 42

using Formula:

$\\\\\bigstar \: \: {\underline{\underline { \boxed{{\textsf {\textbf{\color{blue}{C.S.A of Cylinder = 2πrh}}}}}}}}$

putting values in the formula;

$\\\sf\dashrightarrow 2\times\dfrac{22}{{\cancel{7}}}\times{{\cancel{42}}}\times{120}$

$\sf\dashrightarrow 44\times{6}\times{120}$

$\sf\dashrightarrow 31680\:{cm}^{2}$

hence Area of 1 revolution is 31680 cm² .

Area of 500 revolutions :

→ 31680 × 500

→ 15840000 cm²

In order to convert this number into m², we have to multiply this number with the number $\dfrac{1}{100}\times\dfrac{1}{100}$

$\\\sf\dashrightarrow 15840000\times\dfrac{1}{100}\times\dfrac{1}{100}$

$\sf\dashrightarrow 1584m²$

∴ The area of the playground is 1584m²

Answer 2

Answer:

$\cal\pink{Given :-}$

Diameter of Roller is 84 cm.

Length /Height of Roller is 120 cm.

$\cal\blue{To \:Find :-}$

Area of Playground in m².

$\cal\red{Solution :-}$

$\green\longmapsto\tt{Radius=\dfrac{84}{2}=42\:cm}$

$\green\longmapsto\tt{Height=120\:cm}$

$\cal\orange{Using \: formula :-}$

$\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\pi{rh}}$

$\cal\red{Putting \: values :-}$

$\blue\longmapsto\tt{2\times\dfrac{22}{{\cancel{7}}}\times{{\cancel{42}}}\times{120}}$

$\green\longmapsto\tt{44\times{6}\times{120}}$

$\green\longmapsto\tt\bf{31680\:{cm}^{2}}$

So , Area of 1 revolution is 31680 cm².

Now ,

Area of 500 revolutions :

$\blue\longmapsto\tt{31680\times{500}}$

$\blue\longmapsto\tt\bf{15840000\:{cm}^{2}}$

In m²

$\blue\longmapsto\tt{\dfrac{1584{\cancel{0000}}}{1{\cancel{0000}}}}$

$\blue\longmapsto\tt\bf{1584\:{m}^{2}}$

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