Question

The ratio between the curved surface area and the total surface area of right circular cylinder is 1.2 Find the volume of the cylinderif it's total surface area is 616cm2

Answer 1

Given :-

The ratio between the curved surface area and the total surface area of right circular cylinder is 1:2

To Find :-

Volume

Solution :-

We know that

CSA = 2πrh

TSA = 2πr(r + h)

CSA/TSA = 1/2

2πrh/2πr(r + h) = 1/2

h/r + h = 1/2

2(h) = r + h

2h = r + h

2h - h = r

h = r (1)

Now, ATQ

CSA = TSA/2

CSA = 616/2

CSA = 308 cm

CSA = 2πrh

• As r = h

CSA = 2πrr

CSA = 2πr²

308 = 2 × 22/7 × r²

308 = 44/7 × r²

308 × 7/44 = r²

49 = r²

√(49) = r

7 = r

As r = h

h = 7 cm

Now,

Volume of cylinder = πr²h

Volume = 22/7 × (7)² × 7

Volume = 22/7 × 49 × 7

Volume = 22 × 49

Volume = 1078 cm³

Answer 2

Step-by-step explanation:

Total surface area (T.S.A) = 616 cm^2 Let r be the radius of cylinder and h be the radius of cylinder. 

As per given statement:

(curved surface area / (total surface area) = 1/2 or CSA =   1/2 TSA 

CSA =   1/2 x 616 = 308

=》CSA=308cm^2

Now, 

TSA = 2πrh + 2πr^2 

⇒ 616 = CSA + 2πr^2 

⇒ 616 = 308 + 2πr^2 

⇒ 2πr^2 = 616 – 308 

⇒ 2πr^2 = 308

⇒ r^2 = 308/2π

⇒ r^2 = 49  or r = 7 cm …(1) 

As, CSA = 308 cm^2 

2πrh = 308 

⇒ 2 x 22/7×7 x h = 308 (using (1)) 

⇒ h = 7 cm 

Now, 

Volume of cylinder = πr^2h 

= 22/7 x 7 x 7 x 7  = 1078 

Therefore, Volume of cylinder is 1078 cm2.