Question

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 1

Solution :-

→ Length of roller = 120cm.

→ Diameter of roller = 84cm.

→ Radius of roller = (Diameter)/2 = 84/2 = 42cm.

As we know, a roller is in the shape of a cylinder.

→ Perimeter of roller = Area covered by roller in 1 one revolution = 2 * π * (radius) * Length

→ Perimeter = 2 * (22/7) * 42 * 120

→ Perimeter = 44 * 6 * 120

→ Perimeter = 31,680 cm².

Therefore,

→ Area covered by wheel in 1000 revolutions = (31680 * 1000) cm² = (31680000) / (10000) = 3168m² . (Ans.)

Hence, Area of Playground is 3168m².

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow height(H)= 120cm$

$\sf\dashrightarrow diameter of roller= 84cm$

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

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

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

$\sf\dashrightarrow radius= 42cm$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow AREA\: OF\:PLAYGROUND$

✯.FORMULA IN USE,

$\large{\boxed{\bf{ \star\:\: C.S.A\: OF\: CYLINDER= 2 \pi rh \:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

✯ACCORDING TO THE QUESTION,

$\purple{\text{AREA COVERED BY ROLLER IN 1 REVOLUTION = PERIMETER OF ROLLER}}$

$\sf\therefore AREA \:COVERED \:IN\: ONE\: REVOLUTION= 2 \pi r h$

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

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

$\sf\implies 2 \times 22 \times 6 \times 120$

$\sf\implies 44 \times 72$

$\sf\implies 31680cm^2$

$\large{\boxed{\bf{ \star\:\: 31680cm^2\:\: \star}}}$

$\sf\therefore THE\:ROLLER\:TAKES\:1000\: REVOLUTIONS\:TO\:COVER\:AREA\:OF\:THAT\: PARTICULAR\:PALAYGROUND$

$\sf\therefore we\: know,\: to\: complete\: one \:revolution\: it \:takes \:31680cm^2 \:area$

$\sf\therefore then \:area \:of\:rectangle = 1000 \times the \:area\: in\: one\: complete\: revolution$

$\sf\implies 1000 \times 31680$

$\sf\implies 31680000cm^2$

CONVERSION,

$\sf\therefore cm^2 \:into\:m^2$

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

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

$\sf\implies 3168 m^2$

$\large{\boxed{\bf{ \star\:\: AREA\:OF\: PLAYGROUND= 3168m^2 \:\: \star}}}$

$\large\underline\bold{AREA\:OF\:PLAYGROUND\:IS\:3168cm^2}$

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