Question

The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. Find the diameter and the height of the pillar.

Answer 1

The diameter is 14 m and the height of the pillar is 6 m.

Step-by-step explanation:

Given :

curved surface area of a cylindrical pillar =  264 m² and volume of a cylindrical pillar = 924 m³

CSA of cylinder = 2πrh

264 = 2× 22/7 × r × h

rh = (264 × 7)/44

rh = 1848/44

rh = 42  

h = 42/r ......(1)

Now,  

Volume of cylinder = πr²h

Putting the value of h = 42/r from eq 1 ,  

924 = 22/7 × r² × 42/r

924r = 924 × 7

r = (924 × 7)/7

r = 7 m

Radius , r =  7 m  

Diameter = 2 × radius  =  2 × 7  = 14 m.

Height of the cylinder , h = 42/r = 42/7 = 6 m

Hence, the diameter is 14 m and the height of the pillar is 6 m.

Hope this answer will help you…

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Answer 2

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

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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