Question

the diameter of a roller is 84 cm and its length is 120 cm it takes 500 complete revolution to move once over to level a playground find the area of the playground in metre square ​

Answer 1

Question ⤵️

the diameter of a roller is 84 cm and its length is 120 cm it takes 500 complete revolution to move once over to level a playground find the area of the playground in metre square .

Answer ⤵️

$Radius \: of \: the \: roller (r) = \frac{84}{2} cm=42cm$

length of the roller (h) = 120cm

∴ Area of the playground levelled in taking 1 complete revolution 2πrh

= 2 × 227 × 42 × 120 = 31680cm²

∴ Area of the playground

=31680 × 500 = 15840000cm²

$\frac{15840000}{100 \times 100} { \: m}^{2} = {1584 \: m}^{2}$

Hope it helps you ✌️

Step-by-step explanation:

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Answer 2

Given,

The diameter of a roller is 84 cm and its length is 120 cm it takes 500 complete revolution to move once over to level a playground.

To Find,

The area of the playground in metre².

Solution,

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{42cm}}\put(9,17.5){\sf{120cm}}\end{picture}$

Length of the cylinder (Height) = 120 cm

Diameter of the cylinder = 84 cm

Therefore,

radius = 42 cm

Area covered by the roller in one revolution = CSA of the cylinder

= 2πrh

= 2 x $\dfrac{22}{7}$ x 42 x 120

= 31680cm²

No. of revolutions required to level the complete playground = 500

Therefore,

Total area of playground = Area covered in one revolution x No. of revolutions

= 31680 x 500

15840000 cm²

[In order to convert this number into m², we have to multiply this number with the number $\dfrac{1}{100}\times\dfrac{1}{100}$]

= $15840000\times\dfrac{1}{100}\times\dfrac{1}{100}$

= 1584m²

∴ The area of the playground is 1584m².