Question

1. A solid cylinder has a total surface of 462 cm2 .its curved surface area is 1/3 of total surface area .find the volume of the cylinder.

Answer 1

Hi.

Good question and Be Brainly.

Here is your answer----

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Given---
Total surface area of the solid cylinder(T.S.A) = 462 cm^2
Also, Curved surface area (C.S.A) = (1/3) x Total surface area
                                          = (1/3) x 462
                                          = 154 cm^2
Using the Formula,
   C.S.A = 2 X π X r x h
  2 x π x rh = 154  --------------------------------eq.(1)
    
Also,
  T.S.A = 2 π r(h +r)
    462  = 2 x π x rh + 2π x r^2
 
Using eq(1),

     462  =  154 + 2π x r^2 
   2π x r^2 = 462 - 154
    (22/7) x r^2 = 308
          2 x r^2 = 308 x (7/22)
        2 x r ^2 = 14 x 7
              r^2 = 98/2
              r =  √49
              r = 7 cm 

Again from eq(1),
         2 π x r x h =154
          2 x (22/7) x 7 x h = 154
                           h = 154/44
                                h = 3.5/ cm.
Using the Formula,
   
Volume of the Cylinder = π x r^2 x h
                                        = (22/7) x 7 x 7 x 3.5
                                        = 539 cm^3
                                   ----------------------------------------

Thus, volume of the cylinder is 539 cm^3.

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Hope it will helps u.

Have a nice day.

Answer 2

$\huge{\mathfrak{\red{Answer}}}$

Curved surface area = total surface area / 3.

Curved surface area = 462/3 = 154.

Rest of area = 462 - 154 = 308.

$\longrightarrow$2πr^2 = 308.

$\longrightarrow$r^2 = 308 x 7 / 44 = 49.

$\longrightarrow$r = 7.

2πrh = 154.

h = 154 / 2 x 22 = 7/2.

$\longrightarrow$Volume = πr^2 h = (22/7) x (7^2) x (7/2) = 539.

$\rm Volume = 539 cm^3$