Question

The ratio between the curved surface area and the total surface area of a right cylinder is 1:2 fund the ratio between the height and radius of the cylinder.

Answer 1

Answer:

Height : radius = 1 : 1

Step-by-step explanation:

Let the radius of the cylinder be

'r' and height of the cylinder be 'h' respectively.

Then,

Curved surface area of cylinder =

= 2πrh

C. S. A. of cylinder = 2πrh .....(1)

Total surface area of cylinder =

= 2πrh + 2π•r^2

T. S. A. of cylinder = 2πr(h + r)

..... (2)

Then, ratio of C. S. A. and T. S. A. =>

from eq. (1) and eq. (2) , we get,

CSA/TSA = 2πrh/2πr(h+r)

CSA/TSA = h / (h+r) .... (3)

It is given that,

CSA : TSA = 1:2

CSA/TSA = 1/2 .....(4)

From eq.(3) and eq.(4) , we get,

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

=> 2h = h+r

=> 2h - h = r

=> h = r .... (5)

Now, ratio of height and radius of cylinder respectively, =>

=> height/radius = h/r .... (6)

From eq. (5) and eq. (6) , we get,

=> h/r = r/r = 1/1

Hence,

height : radius = h:r = 1:1

Hence the required ratio = 1:1