Question

the curved surface area of a cylinder is 154cm^2. the total surface area of the cylinder is three times its curved surface area. find the volume of cylinder

Answer 1

Hope this helps you. Thank you

Answer 2

Solution :

Here , for any cylinder it is given that , its total surface area is three times its curved surface area.

This is quite an interesting property.

Let us assume that the cylinder has a radius of r and a height h .

So, the curved surface area become: 2 pi r h

The total surface area becomes 2 pi r h + 2 pi r^2

3 * (Curved Surface Area ) = ( Total Surface Area )

> 3 * ( 2 pi r h ) = 2 pi r ( h + r )

> 6 pi r h = 2 pi r ( h + r)

> 3 h = h + r

> 2h = r

This is going to be an useful result. \

CSA = 2pi rh

> 2 pi ( 2h ) h

> 4 pi h = 154

> 4 * 22/7 h = 154

> 4/7 h = 7

> h = 49/4

r = h/2 = 49/8

Area of the cylinder :

> pi r^2 h

> 22/7 * 49/8 * 49/8 * 49/4

> 1444.35 cm^2 .

This is the required answer.

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