Question

The sum of the radius of the base and height of solid cylinder is 37 cm . If the total surface area of the cylinder is 1628 m2, Find the volume of the cylinder ?

Answer 1

Given,
r+h=37cm
TSA=1628 cm²
2πr(r+h)=1628
2×22/7 × r ×37 = 1628
2×22×r×37×7=1628
r=1628××7/2×22×37
r=7cm
given,
r+h=37
7+h=37
h=37-7
h=30 cm
volume=πr²h
=22/7 ×7×7× 30
= 22×7×7×30/7
=22×7×30
=4620 cm³

Answer 2

Given,
sum radius of cylinder and height of the cylinder(r+h)=37 cm
total surface area of the cylinder(2*pi*r(r+h))              =1628 cm2
volume of cylinder(pi*r2*h)                                          ="x" cm
 
TSA of the cylinder                                                      =2*22/7*37r=1628

22/7*37r=814
1/7*37r=34
37r=34*7
37r=238

r=6.4

r+h=37
6.4+h=37
h=37-6.4
h=30.6

volume of the cylinder =pi*r^2*h

=22/7*6.4^2*30.6
=3939.182 
Hence the volume of the cylinder is 3939.182

Hope it is useful to you