Question

The diameter of a roller is 168cm and its length is 150cm.its takes 500complete revolution s to leve the playgroung find the area of the play ground in square metres

Answer 1

Given:

• The diameter of the roller is 168cm
• The length (i.e height) of the (cylindrical) roller is 150cm.
• It takes 500 revolutions to level the playground.

To be found:

The area of the playground.

First of all, Let's see the steps for the solution-

• If it is taking a total of 500 complete revolutions to ethe playground then we have to find the Curved Surface Area of the cylindrical roller.

Steps-

1. Get radius of the roller from the diameter.
2. Find the CSA of the roller.
3. And find the area of the playground by the given number of revolutions.

$\star \huge{\underline{\red{SOLUTION:}}}$

Radius = Diameter ÷ 2

⇒ Radius of roller = 168 ÷ 2 = 84cm

$\underline{\red{\sf{The\ formula\ for\ finding\ CSA\ of\ cylinder}}}$

$= \bf 2\pi rh\ unit\ sq.$

$= 2 \times \frac{22}{7} \times 84 \times 150$

$= 2 \times 22 \times 12 \times 150$

$= \boxed{79200\ cm\ sq.}$

Now,

1 revolution = 1 × CSA of cylindrical roller

500 revolution = 500 × 79200

= 39600000 cm sq.

Now,

• 1m = 100 cm

• 1m² = 10000cm²

Also,

$1cm = \frac{1}{100}m$

$1cm^{2} = \frac{1}{10000}m^{2}$

Hence,

39600000 cm sq. = 39600000 ÷ 10000

= 3960 m sq.

Answer 2

Radius = diameter by 2

r = 168/2 = 84cm

CSA = 2[tex]\pi[/tex}rh

= 2 * 22/7 * 84 * 150

= 79200cmsq.

Now,

500 revolution = 500*79200

= 39600000cm sq.

= 3960 m sq.