Question

The diameter of a roller, 120cm long is 84cm. It takes 500 complete revolutions to level a Playground. Find the cost of leveling it at
the rate of Rs 25 per sq metre.​

Answer 1

Answer:

surface area of on revolution = 2∏rh

= 2 x 22/ 7 x 60 x 84

now for 500 revolution = 2 x 22/7 x 60 x 84 x 500

=1584 m2

now cost leveling 1 m2 = Rs. 0.30

= for 1584 m2 = 0.30 x 1584 = Rs. 475 . 20

Answer 2

Answer:

The cost of leveling the playground is ₹ 39600.

Step-by-step-explanation:

We have given the dimensions of a roller.

We know that, a roller is cylindrical in shape.

The length of the cylinder means its height.

We have given that,

$\bullet\sf\:Diameter\:(\:d\:)\:=\:84\:cm\\\\\\\bullet\sf\:Height\:=\:120\:cm$

We know that,

$\displaystyle\sf\:Radius\:=\:\dfrac{Diameter}{2}\\\\\\\implies\sf\:r\:=\:\dfrac{d}{2}\\\\\\\implies\boxed{\red{\sf\:r\:=\:\dfrac{84}{2}\:cm}}$

Now,

The roller takes 500 revolutions to level a playground.

It means we have to find curved surface area of the cylinder.

We know that,

$\displaystyle\pink{\sf\:Curved\:surface\:area\:of\:cylinder\:=\:2\:\pi\:r\:h}\\\\\\\implies\sf\:CSA_{cylinder}\:=\:\cancel{2}\:\times\:\dfrac{22}{7}\:\times\:\dfrac{84}{\cancel2}\:\times\:120\\\\\\\implies\sf\:CSA_{cylinder}\:=\:\dfrac{22\:\times\:\cancel{84}\:\times\:120}{\cancel7}\\\\\\\implies\sf\:CSA_{cylinder}\:=\:22\:\times\:12\:\times\:120\\\\\\\implies\sf\:CSA_{cylinder}\:=\:22\:\times\:1440\\\\\\\implies\boxed{\red{\sf\:CSA_{cylinder}\:=\:31680\:cm^2}}$

Now,

$\sf\:Area\:covered\:with\:500\:revolutions\:=\:500\:\times\:31680\\\\\\\implies\boxed{\red{\sf\:Area\:covered\:with\:500\:revolutions\:=\:15840000\:cm^2}}$

Now,

The rate of leveling is ₹ 25 / m².

Here, the cost is given for metres. We have to convert the area from cm to m.

We know that,

$\sf\:1\:m\:=\:100\:cm\\\\\\\implies\sf\:1\:m^2\:=\:10000\:cm^2\\\\\\\implies\sf\:Area\:in\:metres\:=\:\dfrac{1584\cancel{0000}}{1\cancel{0000}}cm^2\\\\\\\implies\sf\:Area\:in\:metres\:=\:1584\:m^2$

Now,

$\displaystyle\sf\:Cost\:of\:leveling\:playground\:=\:Rate\:of\:leveling\:\times\:Area\:of\:playground\\\\\\\implies\sf\:Cost\:of\:leveling\:playground\:=\:25\:\times\:1584\\\\\\\implies\boxed{\red{\sf\:Cost\:of\:leveling\:playground\:=\:Rs\:39600}}$

The cost of leveling the playground is ₹ 39600.