Question

The curved surface area of a cylindrical pillar is 264 sq m and its volume os 396 cubic metre.find the diameter and height of the pillar​

Answer 1

Given:-

• Curved Surface Area of pillar = 264 m²

• Volume of cylinder = 396 m²

To Find:-

• Height of pillar

• Diameter of pillar

Formula Used:-

• Curved Surface Area of Cylinder = 2 πrh

• Volume of Cylinder = πr²h

Here,

▪︎ π = 22/7

▪︎r = Radius

▪︎h = Height

Solution:-

Let the radius be r m

Let the height be h m

Volume of cylinder = πr²h ------ eq. 1

Curved Surface Area of Cylinder = 2πrh ------- eq.2

By dividing eq. i and eq. ii

Volume ÷ C.S.A = 396 ÷ 264

$\tt{\implies \frac{\pi r²h}{2\pi rh} = 1.5}$

$\tt{\implies \frac{\cancel{\pi} × \cancel{r}× r × \cancel{h}}{2\cancel{\pi} \cancel{r} \cancel{h}} = 1.5}$

$\tt{\implies \frac{r}{2} = 1.5}$

$\tt{\implies r}= 1.5 × 2$

$\boxed{\bf {\purple{\therefore diameter = 2r = 6m}}}$

Putting the value of r in eq.2

According to given conditions ;

CSA of Cylinder = 264 m²

$\tt{\implies 2\pi × 3 × h = 264 m²}$

$\tt{\implies 2× \frac{22}{7} × 3 × h = 264 m²}$

$\tt{\implies \frac{ 132h}{7} = 264 m²}$

$\tt{\implies 132h = 264 × 7}$

$\tt{\implies h = 1848 ÷ 132}$

$\boxed{\bf {\purple{\therefore h = Height= 14 m}}}$