area of right circular cylinder

Question

To level the top of the school play ground for the animal sports a hand-drawn roller of diameter 56cm was engaged. A group of students involved in the job found that after making 10 continuous rounds the roller could level an area of 15.84m². Find the length of the roller?

Answer 1

Sam,

 

In this question, we are looking for the length of the roller, this is the value h in the equations you have been working with because the roller is on it's side. Think about a piece of paper that is rolled into a cylinder. has you roll that paper across a desk, it covers a rectangle area.the dimensions of the rectangle on one side is the height of the paper, on the other, it is the circumference of the roll of paper. This is the picture of this problem. 

 

The area of a rectangle is A=L*W

 

A = the area of the rectangle, according to the problem it is 15.84 m²

L = the height of the cylinder, in this problem we do not know this measeure, so let's keep this L

W = ten times the circumference of the cylinder. so 10*(Πd). and d is the measure in the problem as 56 cm.

 

W = 10*(Πd)

W = 10*(Π*56)

W = 10*175.93

W = 1759.3 cm

 

In any area or volume problem, it is important to have the units match, so we divide by 100 to change cm to m therefore

W= 17.593m. 

 

Now we are ready to substitute into the problem.

 

A = L * W

15.84 = L * 17.593                     divide both sides by 17.593

0.90 = L

 

So the length of the cylinder is 0.9m or 90cm

 

Let me know if you need more help on this.