area of right circular cylinder

Question

A closed cylindrical vessel of length 20 cm and diameter 10.5 cm is to be made from a light metal sheet. What is the total area of the sheet required for it?

Answer 1

Dear Sam,

   The cylindrical vessel is closed, so that means we have areas for one circular top and one circular base.   We use the area of a circle and multiply it by two.  Secondly,  if you unrolled the piece around the lid and the base, you would have a rectangle with a length of 20cm and a width, which was a circumference of the top before you unrolled it.  The distance around the top is C=2πrh.  Therefore, the area of this rectangle would be A=L*w= 20*2π(5.25).  See below for the equation of the total surface area:

 

The length=height=20cm       D=10.5 cm          r=D/2  = 5.25 cm

 

question:   What is the total area of the sheet required for it?

 

 

                                         2πr²                          (2πr)h           (Area of rectangle=L*w, where (2πr)=width)

total surface area= two areas of circles   +      area of unrolled piece (rectangular shape)

 

 

 

Total surface Area = 2πr² +2πrh ≅ 2 (3.14) (5.25)²  + 2(3.14)(5.25)(20)     using substitution

 

 

Now, I am going to let you finish this problem.  Note: Your answer will be in cm ² .

 

  If I have helped you, please give me thumbs up.

 

                                                                               Susan C.