Question

09. The diameter of 120 cm long roller is 84 cm. It takes 1000 complete revolutions over once to
level a playground. Find the area of the playground.​

Answer 1

AnswEr :

$\bf{ Given}\begin{cases}\sf{Diameter \:of \:Roller=84 \:cm}\\\sf{Radius \:of \:Roller = \cancel\frac{84}{2}=42\:cm}\\ \sf{Length \:of \:Roller = 120 \:cm} \\ \footnotesize\text{Roller take 1000 complete revolution to level playground.}\\\sf{Area\: of \: Playground=?} \end{cases}$

• Curved Surface Area of Roller :

$\implies \tt CSA = 2\pi r h \\ \\\implies \tt CSA = 2 \times \dfrac{22}{\cancel7}\times \cancel{42 \:cm} \times 120 \:cm \\ \\ \implies \tt CSA = 2 \times 22 \times 6 \:cm \times 120 \:cm\\ \\\implies \tt CSA = 44 \times 720 \:{cm}^{2} \\ \\\implies \green{\tt CSA =31680 \:{cm}^{2} }$

$\rule{300}{1}$

◗ Whenever Roller will Rolled, Only CSA (Curved Surface Area) will touch the Ground.

◗ Area Covered by Roller in One Revolution is CSA i.e. 31680 cm²

◗ Area of the Playground will be Total Area Covered by Roller in 1000 revolutions.

$\rule{300}{2}$

• Area of Playground will be :

$\longrightarrow \tt Area\:of\: Playground=CSA \times Revolutions \\ \\\longrightarrow \tt Area\:of\: Playground=31680 \: {cm}^{2} \times 1000 \\ \\\longrightarrow \tt Area\:of\: Playground= 31680000 \: {cm}^{2} \\\\\quad\scriptsize\maltese \:\: \text{Changing Area into metre ^{2} }\\ \\\longrightarrow \tt Area\:of\: Playground= \dfrac{3168\cancel{0000}}{ \cancel{100 \times100}}\:{m}^{2} \\ \\\longrightarrow \large \boxed{\red{\tt Area\:of\: Playground=3168\:{m}^{2}}}$

⠀

∴ Hence, Area of Playground is 3168 m²

#answerwithquality #BAL

Answer 2

$\bf{\Huge{\underline{\bf{ANSWER\::}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}$

The diameter of 120cm long roller is 84cm. It takes 1000 complete revolutions over once to level a playground.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The area of the playground.

$\bf{\Large{\underline{\bf{\blue{Explanation\::}}}}}$

We have,

• The length of the roller or cylinder = 120cm
• The diameter of the roller = 84cm
• It takes 1000 complete revolutions in a playground.

We know that radius of the circle: $\sf{\frac{Diameter}{2} }$

→ Radius of the roller or cylinder = $\sf{\cancel{\frac{84}{2} cm}}$

→ Radius of the roller or cylinder = 42cm.

Therefore,

Area of roller = Curved surface area of cylinder.

Formula of the curved surface area of cylinder: $\sf{\red{2\pi rh}}$

→ Area of roller = $\sf{(2*\frac{22}{7} *42*120)cm^{2} }$

→ Area of roller = $\sf{(2*\frac{22}{\cancel{7}} *\cancel{42}*120)cm^{2} }$

→ Area of roller = (2 × 22 × 6 × 120)cm²

→ Area of roller = 31680cm²

Now,

⇒ Area of 1 revolution = area of roller = 31680cm²

⇒ Area of 1000 revolution = (1000 × 31680)cm²

⇒ Area of 1000 revolution = 31680000cm².

Thus,

The area of the playground is 31680000cm².