Question

the diameter of a roller is 84cm and its length is 120 cm It takes 500 complete revolutions to move once cover to level a playground.find area of playground in m²​ .plsss helpp

Answer 1

Step-by-step explanation:

d = 84 cm

r = 42cm = 0.42m

h = 120 cm = 1.2m

c.s.a. of cylindrical roller = =2×22/7×0.42×1.2

=2×22×0.6×1.2

=3.168 m^2

As it takes 500 revolutions, so multiply the area of roller by 500

3.168×500

=1584 m^2

Hence the roller covers 1584 m^2 of area in 500 revolutions

Answer 2

$\bf{\underline{\underline \blue{Solution:-}}}$

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

• The area of the playground in metre = 1584 m²

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

• The diameter of a roller is 84cm and its length is 120 cm. It takes 500 complete revolutions to move once cover to level a playground.

$\sf\underline{\red{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The area of the playground in metre = ?

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

$\sf\underline{\red{\:\:\: Formula\:used\: here:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Curved \: surface \:area \:of\: the\: roller = 2\pi rh }$

$\sf\underline{\red{\:\:\: Now,Putting\:the\: values:-\:\:\:}}$

$\dashrightarrow \sf {\Bigg(2 \times \frac{22}{7} \times 42 \times 120\Bigg) \:Cm^2}$

$\dashrightarrow \sf {\Bigg(264 \times 120\Bigg)\:Cm^2}$

$\dashrightarrow \sf {31680 \: Cm^2}$

$\sf\underline{\red{\:\:\: ThereFore:-\:\:\:}}$

• Area covered by the roller in 1 revolution is 31680 cm².

$\sf\underline{\green{\:\:\: Now:-\:\:\:}}$

➪Area covered by the roller in 500 revolutions = $\sf {31680 \times 500\:Cm^2}$

➪Area covered by the roller in 500 revolutions = $\sf {15840000\:Cm^2}$

$\sf\underline{\red{\:\:\: ThereFore:-\:\:\:}}$

• Area covered by the roller in 500 revolutions is 15840000 cm².

$\sf\underline{\green{\:\:\: Thus:-\:\:\:}}$

$\dashrightarrow \textbf {Area of the playground =}$ $\sf {\frac{15840000}{100 \times 100} }$

$\dashrightarrow \textbf {Area of the playground =}$ $\sf {1584\:m^2}$

$\sf\underline{\red{\:\:\: Hence:-\:\:\:}}$

• The area of the playground in metre is 1584 m².

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