Question

thanks for the answer

Answer 1

Here is your solution

Given that:-

Curved surface area : Total surface area = 1:2

 Curved surface area : 616 = 1:2 

Curved surface area = 616 / 2 = 308

 2πrh / 2πr(h+r) = 1/2
 h / (h+r) = 1/2
 h+r = 2h
 ⇒ h = r
Curved surface area  2πr^2 = 308 [Since h = r] 

2 x 22/7 x r^2 = 308 r2 
=> 308 x 7/44 r^2 = 49
=> r = 7 cm 
=> h = 7 cm 

Volume of the cylinder = πr^2h =22/7 x 7 x 7 x 7 
= 1078 cm3

Hence,

Volume of the cylinder is 1078 cu cm.

Hope it helps you

Answer 2

Solutions :-

Given :

The ratio between curved surface and the total surface area of the cylinder = 1 : 2

Total surface area of cylinder = 616 cm²

Let the curved surface area of the cylinder be x

Find the curved surface area of the cylinder :-

=> x/616 = 1/2

=> x × 2 = 1 × 616

=> 2x = 616

=> x = 616/2 = 308

Now,

We know,

Curved surface area of the cylinder = 2 πrh

Total surface area of the cylinder = 2 πr(r + h)

=> 2πrh / 2πr(r + h) = 1/2

=> h / (h+r) = 1/2

=> h+r = 2h

 => h = r

Curved surface area = 2πrh

 = 2πr² = 308 [Since h = r] 

=> 2 x 22/7 x r² = 308 

=> 6.28 r² = 308

=> r² = 308/6.28

=> r² = 49

=> r = √49 = 7

So, r = h = 7

Final the volume of the cylinder :-

Volume of the cylinder = πr²h 

=22/7 x 7² × 7 

= 1078 cm³

Hence,

The Volume of the cylinder is 1078 cm³