Question

A cylindrical roller rolls over 400 times to completely cover a sport ground if the length of roller radius is 1.4 and length is 3.5 then find the area of the field

Answer 1

Area in one round = 2*pi*1.4*3.5 = 30.787.

In 400 turns =400*30.787

Area = 12315.04.

Answer 2

If the length of roller radius is 1.4 and length is 3.5 then the area of the field is 12320 unit square.

Step-by-step explanation:

Given dimensions of the cylindrical roller:

Length, h = 3.5 unit

Radius, r = 1.4 unit

We know that,

[The distance travelled by the roller in 1 roll] = [Curved surface area of the cylinder] = 2πrh

So, the distance travelled by the roller when it rolls for 1 time = 2 * $\frac{22}{7}$ * 1.4 * 3.5 = 30.8 unit square.

Now, it is given that the cylindrical roller rolls for 400 times to completely cover the sports ground.

Therefore, we get

The area covered by the roller in rolling for 400 times will be,

= 400 * [distance travelled by the roller when it rolls for 1 time]

= 400 * 30.8

= 12320 unit square

Thus, the area of the sports field is 12320 square unit.

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