Question

For the following exercises, find the dimensions of the right circular cylinder described.

The radius is 1/3 meter greater than the height. The volume is 98/9ππ cubic meters.

Answer 1

To find the dimensions of the right circular cylinder,

Consider the following expression provided in the text book.

Consider that the height is h,

Radius will be as follow:

R = (h + 1/3) meters

 

Use the volume is determined as follow:

(98/9)π = πr2h

 (98/9)π = π(h + 1/3) × h

      98/9 = (h2 + 1/9 + 2/3h) × h

      98/9 = h3 + h/9 + 2/3h2

 

Therefore,

h3 + 2/3h2 + h/9 – 98/9 = 0

 

Use maple to solve for the above equation as below:

h3 + 2/3h2 + h/9 – 98/9 = 0

 

Solve for h:

[(h – 2), (h = -4/3 + 1/3 I√33), (h = -4/3 – 1/3 I√33)]

 

Hence, the dimension of the height is 2 meter.

 

Radius will be as follow:

R = (h + 1/3) meters

 

Therefore,

R = (2 + 1/3) meters

   = 7/3 meters

 

Hence, the dimension of the height is 7/3 meters.

Now, volume is πr2h

 

Therefore,

πr2h = 3.14 × 2 × 7/3

          = 14.654

Hence, the dimension of the volume is 14.654 meters.

Hence, the dimension of the volume is 14.654 meters.