Question

The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm square. Find the height and the volume of the cylinder.

Answer 1

Let r and h be the radius and height of the solid cylinder.
r+h=37cm
TSA of cylinder =1628cm^2
2*pie*r(r+h)=1628cm^2
2*pie*r(37)=1628
2*22/7*r*37=1628
r=1628*7/44*37
r=7cm
r+h=37cm
7+h=37cm
h=37-7
h=30cm
Volume of cylinder=πr^2h
=22/7*7*7*30
=210*22
=4620cm^3
Thus, the volume of cylinder is 4620cm^3.
I hope,this answer is helpful

Answer 2

the height is 30cm volume is 4620cm^3

refer the attachment for the method to the question