Question

the diameters and heights of two solid cylinders are 8,3(h-1)units and 12,(h+5)units respectively.if the volumes of these be same,then the value of h is options are (a)9,(b)12,(c)17 and (d)19

Answer 1

Question:

The diameters and heights of two solid cylinders are 8,3(h-1)units and 12,(h+5)units respectively. If the volumes of these be same, then the value of h is :

(a)9

(b)12

(c)17

(d)19

Answer:

Option (d)

h = 19

Note:

If "R" and "H" are the radius and height of a cylinder then ;

• Curved surface area is given as ;

C.S.A. = 2πRH

• Total surface area is given as ;

T.S.A. = 2πR•(R+H)

• Volume is given as ;

V = πR²H

• Radius = Diameter/2

Solution:

It is given that ,

The diameters and heights of two solid cylinders are 8,3(h-1)units and 12,(h+5)units respectively.

Thus,

For 1st cylinder , we have ;

Diameter , D1 = 8

=> Radius , R1 = 8/2 = 4

Height , H1 = 3(h-1)

Hence,

The volume of 1st cylinder will be ;

V1 = π(4)²•3(h-1)

Also,

For 2nd cylinder , we have ;

Diameter , D2 = 12

=> Radius , R2 = 12/2 = 6

Height , H2 = h+5

Hence,

The volume of 1st cylinder will be ;

V2 = π(6)²•(h+5)

Now,

According to the question,

Volumes of both the cylinders are equal.

Thus,

=> V1 = V2

=> π(4)²•3(h-1) = π(6)²•(h+5)

=> 4²•3(h-1) = 6²•(h+5)

=> 48•(h-1) = 36•(h+5)

Dividing both sides by 12 , we get ;

=> 4•(h-1) = 3•(h+5)

=> 4h - 4 = 3h + 15

=> 4h + 3h = 15 + 4

=> h = 19

Hence,

The required value of h is 19 .