The total surface area of a cylinder is 352 cm square. If its height i

1.	The total surface area of a cylinder is 352 cm square. If its height is 10 cm, then find the diameter of the base
Answer» Given : Total Surface Area of Cylinder is 352 cm² . Height of Cylinder is 10 cm . To Find : Diameter of Base . Solution : $\longmapsto\tt{Height=10\:cm}$ Using FoRmula : $\longmapsto\tt\boxed{T.S.A\:of\:Cylinder=2\pi{r(r+h)}}$ Putting Values : $\longmapsto\tt{352=2\times\dfrac{22}{7}\times{r}\times{(r+10)}}$ $\longmapsto\tt{352\times{7}=44\times{{r}^{2}}+10r}$ $\longmapsto\tt{\cancel\dfrac{2464}{44}={r}^{2}+10r}$ $\longmapsto\tt{56={r}^{2}+10r}$ $\longmapsto\tt{{r}^{2}+10r-56}$ By Splitting Middle Term : $\longmapsto\tt{{r}^{2}+(14r-4r)-56}$ $\longmapsto\tt{{r}^{2}+14r-4r-56}$ $\longmapsto\tt{r(r+14)-<klux>4</klux>(r+14)}$ $\longmapsto\tt{(r-4)\:\:(r+14)}$ r = 4 r = -14 Radius of Cylinder can not be negative . So , we will take Radius as 4 cm ... Now , As we know that Diameter id double of Radius . So , $\longmapsto\tt{Diameter=2r}$ $\longmapsto\tt{2(4)}$ $\longmapsto\tt\bf{8\:cm}$ So , Diameter of Cylinder is 8 cm ...