Answer:
4618.14[tex]m^{3}[/tex] or 4618[tex]m^{3}[/tex]
Step-by-step explanation:
From T.S.A = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex][tex]r^{2}[/tex]
where T.S.A = 1628[tex]m^{2}[/tex]
1628 = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex][tex]r^{2}[/tex]
1628 = ( rh + [tex]r^{2}[/tex] ) 2[tex]\pi[/tex]
by dividing both side by 2[tex]\pi[/tex]
[tex]\frac{1628}{2\pi }[/tex]= rh + [tex]r^{2}[/tex]
259.10 = rh + [tex]r^{2}[/tex]
rh = 259.10 - [tex]r^{2}[/tex]
h = [tex]\frac{259.10 - r^{2} }{r}[/tex] (1)
From Radius + Height = 37
r + h = 37 (2)
by substituting eqn 1 into 2
r + [tex]\frac{259.10 - r^{2} }{r}[/tex] = 37
by multiplying r to both side
[tex]r^{2}[/tex] + 259.10 - [tex]r^{2}[/tex] = 37r
259.10 = 37r
r = [tex]\frac{259.10}{37}[/tex]
r = 7.00 ≅ 7
From Eqn 2
r + h = 37
7 + h = 37
h = 37 - 7
h = 30
so Volume of a cylinder = [tex]\pi r^{2} h[/tex]
V = [tex]\pi[/tex] * [tex]7^{2}[/tex] * 30
V = 4618.14[tex]m^{3}[/tex] ≅ 4618[tex]m^{3}[/tex]
