Question

The curved surface area of a cylindrical pillar is 264m^2 and its volume is 924^3. Find the diameter and height of the pillar .​

Answer 1

$\huge \underline \mathsf \red {SOLUTION:-}$

Given That:

• Curved surface area of cylinder = 264 m²
• Volume of cylinder = 924 m³

We know that,

• CSA of cylinder = 2πrh

So,

➠ 264 = 2 × 22/7 × r × h

➠ r × h = (264 × 7)/44

➠ r × h = 1848/44

➠ r × h = 42

➠ h = 42/r ……(1)

Now,

• volume of cylinder = πr²h

Substituting the value of h = 42/r in the volume equation, we get

➠ 924 = 22/7 × r² × 42/r

➠ 924r = 924 × 7

➠ r = 7 m

So,

Radius is 7 m and the diameter will be

= 7 × 2

= 14 m.

And the height of the cylinder

= h = 42/r

= 42/7

= 6 m

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Answer 2

$\huge\bigstar\underline\mathcal\blue{ANSWER:-}$$<font color = blue>$

Given:

CSA of cylindrical pillar = 264m^2

Volume of the cylindrical pillar = 924m^3

Let the radius be r and height be h..

CSA of the pillar = 2πrh

= 264 = 2 × 22/7 × r × h

= 264 = 44/7 × rh

= 264 × 7/44 = rh

= 42 = rh -----(i)

Now, volume of the cylindrical pillar = πr^2h

= 924 = 22/7 × r × r × h

= 924 × 7/22 = r × r× h

= 294 = r × r × h

= 294 = r × 42

as from equation (i) we get rh = 42

= 294/42 = r

7 = r

Therefore, radius (r) is 7m.

And from equation (i),

= 42 = rh

= 42 = 7×h

= 42/7 = h

= 6 = h

Therefore, height = 6m.

Hence, diameter = 2 × r = 2×7 = 14m

and height = 6m