Question

The diameter of a roller is 84cm and its length is 120cm. it takes 500 complete revolutions to move once over a level playground, then the covered area in m square is a​

Answer 1

$\large\red{\tt{\mathcal{QUESTION:}}}$

The diameter of a roller is 84cm and its length is 120cm. it takes 500 complete revolutions to move once over a level playground, then the covered area in m square is a.

$\large\red{\tt{\mathcal{ANSWER:}}}$

Given:-

Diameter = 84cm

Radius = ${\frac{84}{2}$ = 42cm

Length = 120cm

T.S.A of cylinder = 2πrh

= 2 x 22/7 x 42 x 120

= 31680 cm²

Area levelled by 500 revolution = Area of playground

=> 500 x 31680cm²

=> 15840000 cm²

Which is the required answer.

${\huge{\underline{\small{\mathbb{\blue{HOPE\:HELP\:U\:BUDDY :)}}}}}}$

${\huge{\underline{\small{\mathbb{\pink{</p><p>~cαndчflσѕѕ♡ :)}}}}}}$

Answer 2

Answer:

$\huge{\mathfrak{\red{Answer}}}$

$\sf\red \dashrightarrow \purple{diameter of roller= 84cm}$

$\sf\blue \therefore \green{radius= \dfrac{diameter}{2}}$

$\sf\red \dashrightarrow \orange{ \dfrac{84}{2}}$

$\sf\purple \dashrightarrow \pink{\cancel \dfrac{84}{2}}$

$\sf\green \dashrightarrow \blue{radius= 42cm}$

$\large\underline\mathfrak{\purple{TO\:FIND,}}$

$\sf\orange \dashrightarrow \red{AREA\: OF\:PLAYGROUND }$

$\sf \blue {ƒσɾɱµℓα}$

$\rm{\boxed{\sf{ c.s.α\: σƒ \: cყℓเɳ∂εɾ = 2 \pi rh}}}$

$\large\underline\mathtt{\purple{sσℓµƭเσɳ,}}$

$\purple{\text{αɾεα\: cσѵεɾε∂\: ɓყ \:ɾσℓℓεɾ\: เɳ \:1\: ɾεѵσℓµƭเσɳ}}$

$\blue \implies \green{ρεɾเɱεƭεɾ \:σƒ\: ɾσℓℓεɾ}$

$\sf\purple \therefore \pink{αɾεα \:cσѵεɾε∂ \:เɳ \: σɳε \: ɾεѵσℓµƭเσɳ = 2 \pi r h}$

$\sf\orange \implies \red{ 2 \times \dfrac{22}{7} \times 42 \times 120}$

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

$\sf\orange \implies \red{2 \times 22 \times 6 \times 120}$

$\sf\green \implies \blue{ 44 \times 72 }$

$\sf\purple \implies \pink{ 31680cm^2 }$

$\rm{\boxed{\sf{ 31680cm^2}}}$

$\sf\therefore \purple{ ƭɦε \:ɾσℓℓεɾ \:ƭαҡεs \:1000\: ɾεѵσℓµƭเσɳ\: ƭσ \:cσѵεɾ \:αɾεα \:σƒ \:ƭɦαƭ\: ραɾƭเcµℓαɾ\:ρℓαყ\: ɠɾσµɳ∂}$

$\sf\green \therefore \blue{ωε \: ҡɳσω,\: ƭσ \: cσɱρℓεƭε \: σɳε \:ɾεѵσℓµƭเσɳ \: เƭ \:ƭαҡεs \:31680cm^2 \:αɾεα }$

$\sf\orange \therefore \red{ƭɦεɳ \:αɾεα \:σƒ \:ɾεcƭαɳɠℓε = 1000 \times ƭɦε \:αɾεα \: เɳ \: σɳε \: cσɱρℓεƭε \: ɾεѵσℓµƭเσɳ }$

$\sf\purple \implies \pink{ 1000 \times 31680 }$

$\sf\blue \implies \green{31680000cm^2}$

$\sf\pink \therefore \purple{cm^2 \:into\:m^2}$

$\sf\red \therefore \orange{\dfrac{ 31680000}{ 100 \times 100}}$

$\sf\orange \implies \red{\cancel \dfrac{ 31680000}{ 100 \times 100}}$

$\sf\red \implies \orange{3168 m^2}$

$\sf\purple { αɾεα \:σƒ \: ρℓαყɠɾσµɳ∂ = 3168m^2}$

$\sf \red\therefore \blue {αɾεα \:σƒ \:ρℓαყ\:ɠɾσµɳ∂ \:เs \:3168cm^2}$