.the diameter of a 120 cm long roller is 84 cm It takes 1000 complete revolutions in moving once over to level a playground what is the area of the playground
Answers
Answer:
Answer✍︎
\large\underline\mathfrak{\red{GIVEN,}}
GIVEN,
\sf\dashrightarrow \blue{height(H)= 120cm }⇢height(H)=120cm
\sf\dashrightarrow \blue{diameter of roller= 84cm}⇢diameterofroller=84cm
\sf\therefore \blue{radius= \dfrac{diameter}{2}}∴radius=
2
diameter
\sf\dashrightarrow \blue{ \dfrac{84}{2}}⇢
2
84
\sf\dashrightarrow \blue{\cancel \dfrac{84}{2}}⇢
2
84
\sf\dashrightarrow \blue{radius= 42cm}⇢radius=42cm
\large\underline\mathfrak{\purple{TO\:FIND,}}
TOFIND,
\sf\dashrightarrow \red{AREA\: OF\:PLAYGROUND }⇢AREAOFPLAYGROUND
FORMULA
\rm{\boxed{\sf{ \circ\:\: C.S.A\: OF\: CYLINDER= 2 \pi rh \:\: \circ}}}
∘C.S.AOFCYLINDER=2πrh∘
\large\underline\mathtt{\purple{SOLUTION,}}
SOLUTION,
© ATQ,
\purple{\text{AREA COVERED BY ROLLER IN 1 REVOLUTION = PERIMETER OF ROLLER}}AREA COVERED BY ROLLER IN 1 REVOLUTION = PERIMETER OF ROLLER
\sf\therefore \pink{AREA \:COVERED \:IN\: ONE\: REVOLUTION= 2 \pi r h}∴AREACOVEREDINONEREVOLUTION=2πrh
\sf\implies \red{ 2 \times \dfrac{22}{7} \times 42 \times 120}⟹2×
7
22
×42×120
\sf\implies \blue{ 2 \times \dfrac{22}{\cancel{7}} \times \cancel{42} \times 120}⟹2×
7
22
×
42
×120
\sf\implies \red{2 \times 22 \times 6 \times 120}⟹2×22×6×120
\sf\implies \blue{ 44 \times 72 }⟹44×72
\sf\implies \pink{ 31680cm^2 }⟹31680cm
2
\rm{\boxed{\sf{ \circ\:\: 31680cm^2\:\: \circ}}}
∘31680cm
2
∘
\sf\therefore \purple{ THE\:ROLLER\:TAKES\:1000\: REVOLUTIONS TO\:COVER\:AREA\:OF\:THAT\: PARTICULAR\:PALAYGROUND}∴THEROLLERTAKES1000REVOLUTIONSTOCOVERAREAOFTHATPARTICULARPALAYGROUND
\sf\therefore \blue{we\: know,\: to\: complete\: one \:revolution\: it \:takes \:31680cm^2 \:area }∴weknow,tocompleteonerevolutionittakes31680cm
2
area
\sf\therefore \red{then \:area \:of\:rectangle = 1000 \times the \:area\: in\: one\: complete\: revolution}∴thenareaofrectangle=1000×theareainonecompleterevolution
\sf\implies \pink{ 1000 \times 31680 }⟹1000×31680
\sf\implies \green{31680000cm^2}⟹31680000cm
2
CONVERSION,
\sf\therefore \green{cm^2 \:into\:m^2}∴cm
2
intom
2
\sf\therefore \blue{\dfrac{ 31680000}{ 100 \times 100}}∴
100×100
31680000
\sf\implies \red{\cancel \dfrac{ 31680000}{ 100 \times 100}}⟹
100×100
31680000
\sf\implies \orange{3168 m^2}⟹3168m
2
\rm{\boxed{\sf{ \circ\:\: AREA\:OF\: PLAYGROUND= 3168m^2 \:\: \circ}}}
∘AREAOFPLAYGROUND=3168m
2
∘
\rm\underline\mathrm{AREA\:OF\:PLAYGROUND\:IS\:3168cm^2}
AREAOFPLAYGROUNDIS3168cm
2
Answer:
Thanks for free points bro
justice for Sushant bhaiya