.the diameter of a 120 cm long roller is 84 cm It takes 1000 complete

1.	.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
Answer» $\huge\mathtt{\fbox{\red{Answer✍︎}}}$ $\large\underline\mathfrak{\red{GIVEN,}}$ $\sf\dashrightarrow \blue{height(H)= 120cm }$ $\sf\dashrightarrow \blue{diameter of roller= 84cm}$ $\sf\therefore \blue{radius= \dfrac{diameter}{2}}$ $\sf\dashrightarrow \blue{ \dfrac{84}{2}}$ $\sf\dashrightarrow \blue{\cancel \dfrac{84}{2}}$ $\sf\dashrightarrow \blue{radius= 42cm}$ $\large\underline\mathfrak{\purple{TO\:FIND,}}$ $\sf\dashrightarrow \red{AREA\: OF\:PLAYGROUND }$ FORMULA $\rm{\boxed{\sf{ \circ\:\: C.S.A\: OF\: CYLINDER= 2 \pi rh \:\: \circ}}}$ $\large\underline\mathtt{\purple{SOLUTION,}}$ © ATQ, $\purple{\text{AREA COVERED BY ROLLER IN 1 REVOLUTION = PERIMETER OF ROLLER}}$ $\sf\therefore \pink{AREA \:COVERED \:IN\: ONE\: REVOLUTION= 2 \pi r h}$ $\sf\implies \red{ 2 \times \dfrac{22}{7} \times 42 \times 120}$ $\sf\implies \blue{ 2 \times \dfrac{22}{\cancel{7}} \times \cancel{42} \times 120}$ $\sf\implies \red{2 \times 22 \times 6 \times 120}$ $\sf\implies \blue{ 44 \times 72 }$ $\sf\implies \pink{ 31680cm^2 }$ $\rm{\boxed{\sf{ \circ\:\: 31680cm^2\:\: \circ}}}$ $\sf\therefore \purple{ THE\:ROLLER\:TAKES\:1000\: REVOLUTIONS TO\:COVER\:AREA\:OF\:THAT\: PARTICULAR\:PALAYGROUND}$ $\sf\therefore \blue{we\: know,\: to\: complete\: one \:revolution\: it \:takes \:31680cm^2 \:area }$ $\sf\therefore \red{then \:area \:of\:rectangle = 1000 \times the \:area\: in\: one\: complete\: revolution}$ $\sf\implies \pink{ 1000 \times 31680 }$ $\sf\implies \green{31680000cm^2}$ CONVERSION, $\sf\therefore \green{cm^2 \:into\:m^2}$ $\sf\therefore \blue{\dfrac{ 31680000}{ 100 \times 100}}$ $\sf\implies \red{\cancel \dfrac{ 31680000}{ 100 \times 100}}$ $\sf\implies \orange{3168 m^2}$ $\rm{\boxed{\sf{ \circ\:\: AREA\:OF\: PLAYGROUND= 3168m^2 \:\: \circ}}}$ $\rm\underline\mathrm{AREA\:OF\:PLAYGROUND\:IS\:3168cm^2}$