Question

Question #9ab18

Answer 1

`137984cm^3`

Explanation:

Let the radius of the right circular cylinder be r cm
and height be h cm

The area of its Curved Surface =`2pirh` cm^2

The area of its Plane Crcular Surface =`2pir^2` cm^2

So The area of its Total Surface =`(2pir^2+2pirh)` cm^2

By the 1st condition of the problem:
The ratio of total surface area to the curved surface area of a right circular cylinder is 3 : 2
Hence
`(2pir^2+2pirh)/(2pirh)=3/2=>((cancel(2pir)(r+h))/(cancel(2pir)h))=3/2`
`=>(r+h)/h=3/2`
`=>3h=2r+2h`
`=>h=2r`

Now by the 2nd condition of the problem:

Total surface area = 14784 cm^2
So `(2pir^2+2pirh)= 14784`
`=>(2pir^2+2pir*2r)= 14784` [ putting h=2r ]
`=>(2pir^2+4pir^2)= 14784`
`=>(6pir^2)= 14784`
`=>(6*22/7r^2)= 14784`

`=>r^2= cancel(14784)^112*7/cancel22*1/cancel6=16*7*7`
`r=sqrt(4^2*7^2)=28cm`

Hence Radius of the Cylinder = r=28 cm

So its height `h=2r=2xx28cm=56cm`

and Volume of the Cylinder =`pir^2h=22/7*28^2 *56 cm^3`
`=22/cancel7*cancel28^4*28 *56 cm^3=137984 cm^3`