Question

The value of the surface area of the cylinder is equal to the value of the volume of the cylinder. Find the value of x .

diameter is 71/5 ft height is x ft

Answer 1

Given

Diameter  =  71/5 ft

Then Radius (r)  =  (71/5) /2 = 71/10 ft

And Height (h)  =  x ft

The surface area of the Cylinder =  2πr^2 + 2πrh

The volume of the cylinder = π(r^2)h

And also given that The value of the surface area of the cylinder is equal to the value of the volume of the cylinder

Hence,

2πr^2 + 2πrh = π(r^2)h

π[ 2r^2 + 2rh ]  = π(r^2)h

2r^2 + 2rh  =  hr^2

2r^2  =  hr^2 - 2rh

2r^2  =  h(r^2 - 2r)

h  =  (2r^2) / (r^2 - 2r)

h  =  (2r^2) / r^2(1 - 2/r)

h  =   2 / (1 - 2/r)

Substitute h = x and r = 71/10 in above equation

x  =   2 / [ 1 - 2 / (71/10) ]

x  =   2 / [ 1 - 20 / 71 ]

x  =   2 / [ (71 - 20) / 71 ]

x  =   2 X 71 / 51

x  =   142 / 51 ft

Answer :

x  =   142 / 51 ft