Question

HELP ASAP!!!!!!The ratio of the curved surface area of a right circular cylinder is 1 : 3. Find the volume of the cylinder if its total surface area is 1848cm^2..
PLS BHAI AND BEHAN LOG.
ANSWER IT!!!!!✌✌

Answer 1

The ratio of the curved surface area of a right circular cylinder and volume is 1 : 3. Find the volume of the cylinder if its total surface area is 1848cm².
Given:
 
Ratio of CSA and Volume of a right circular cylinder=1:3

TSA of right circular cylinder=1848 cm²

Then,
 
                                2πr(h+r)=1848 cm²                                               --------1

CSA of right circular cylinder/volume of right circular cylinder=1/3
             
                                                                                 2πrh/πr²h=1/3
              
                                                                                             2/r=1/3
              
                                                                                                r=6 cm    -------2

From 1 and 2

          2πr(h+r)=1848

2×22/7×6(h+6)=1848

                 h+6=1848×7/22×2×6

                      h=49-6     ⇒  h=43 cm

As we obtained r=6 cm and h=43 cm

Then Volume of cylinder=πr²h
   
                                       =22×6×6×43/7

                                       =4865.14 cm² (approx)

Answer 2

We know that C.S.A = 2pirh.

We know that T.S.A  = 2pir(r + h).

Given that ratio of C.S.A to T.S.A = 1/3.

1/3 = 2pirh/2pir(r + h)

1/3 = h/r + h

r + h = 3h

r = 2h  ----- (1)



Given that T.S.A = 1848cm^2.

2pir(r + h) = 1848

2 * 22/7 * 2h(2h + h) = 1848

2 * 22/7 * 2h(3h) = 1848

2 * 22/7 * 6h^2 = 1848

2 * 22 * 6h^2 = 1848 * 7

44 * 6h^2 = 12936

264h^2 = 12936

h^2 = 12936/264

h^2 = 49

h = 7cm.


Substtute h = 7 in (1), we get

r = 2 * 7

r = 14cm.


Now,


Volume of cylinder = pir^2h

                                = 22/7 * (14)^2 * 7

                                = 22 * 196

                                = 4312cm^3.



Therefore, the volume of the cylinder = 4312cm^3.


Hope this helps!