Question

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 1

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 :

$\longmapsto\tt{{r}^{2}+(14r-4r)-56}$

$\longmapsto\tt{{r}^{2}+14r-4r-56}$

$\longmapsto\tt{r(r+14)-4(r+14)}$

$\longmapsto\tt{(r-4)\:\:(r+14)}$

• 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 ...