Question #9ab18

1 Answer
May 7, 2016

Answer:

#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#