Question

The sum of the radius of the base and the height of a solid cylinder is 37m. If the total surface area of the cylinder is 1628 m^2, find its volume
PLEASE HELP

Answer 1

Answer:

920

Step-by-step explanation:

Answer 2

Answer:

4618.14$m^{3}$ or 4618$m^{3}$  

Step-by-step explanation:

From  T.S.A = 2$\pi$rh + 2$\pi$$r^{2}$

 where T.S.A = 1628$m^{2}$

           1628 = 2$\pi$rh + 2$\pi$$r^{2}$

            1628 =  ( rh + $r^{2}$ ) 2$\pi$

 by dividing both side by 2$\pi$

             $\frac{1628}{2\pi }$=  rh + $r^{2}$

          259.10 = rh + $r^{2}$

           rh = 259.10 - $r^{2}$

        h = $\frac{259.10 - r^{2} }{r}$            (1)

From Radius + Height = 37

       r + h = 37                (2)

by substituting eqn 1 into 2

    r + $\frac{259.10 - r^{2} }{r}$   = 37

by multiplying r to both side

   $r^{2}$ + 259.10 - $r^{2}$ = 37r

     259.10 = 37r

   r = $\frac{259.10}{37}$

   r = 7.00 ≅ 7  

From Eqn 2

     r + h = 37

     7 + h = 37

     h = 37 - 7

     h = 30

so Volume of a cylinder = $\pi r^{2} h$

                  V = $\pi$ * $7^{2}$ * 30

                  V = 4618.14$m^{3}$  ≅  4618$m^{3}$