The sum of the height and radius of the solid cylinder is 37m.If the t

1.	The sum of the height and radius of the solid cylinder is 37m.If the total surface area of the cylinder be1628msq,find it's volume
Answer» ANSWER : Volume of the cylinder is 4620 m³. EXPLANATION : GIVEN :- SUM of height and radius of the solid cylinder = 37 m. Total SURFACE area of the cylinder = 1628 m². TO FIND : Volume of cylinder. SOLUTION : Let the height of the cylinder be h m and the radius of the cylinder be r m. Sum of height and radius= 37 m. Total surface area = 1628 m². We know, TSA of cylinder = 2πr(h+r) According to the question, $\sf{h+r=37............(i)}$ $\sf{2\pi\:r(h+r)=1628............(ii)}$ ✪Taking EQ(ii)✪ $\sf{2\pi\:r(h+r)=1628}$ $\implies{2\times\frac{22}{7}\times\:r\times\:37=1628\:\:[From\:eq(i)\:h+r=37]}$ $\implies\sf{r=1628\times\:\frac{1}{2}\times\:\frac{7}{22}\times\:\frac{1}{37}}$ $\implies\sf{r=7}$ † Putting r = 7 in eq .(i) † h +r = 37 →h + 7 = 37 →h = 37 - 7 → h = 30 Radius = 7 m. Height = 30 m. We know, Volume of cylinder= πr²h $\sf{\:\:\:Volume\: of\: cylinder=\pi\:r^2h}$ $\implies\sf{Volume\: of\: cylinder=\frac{22}{7}\times\:7\times\:7\times\:30\:m^3}$ $\implies\sf{Volume\:of\: cylinder=4620\:m^3}$ Therefore, volume of the cylinder is 4620 m³. ____________________