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

$\huge\underline\mathrm{SOLUTION:-}$

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

Question

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

Solution

Given:-

• The curved surface area of a cylindrical pillar is 264 m²
• volume of cylindrical pillar 924 m³ .

Find:-

• Diameter & height of the cylindrical pillar .

Explanation

Using Formula

☛ Curved Surface area of cylindrical pillar = 2πrh

☛ Volume of cylindrical pillar = πr²h

So,

➥ Curved Surface area of cylindrical pillar = 2πrh

➥ 264 = 2πrh

➥ 2 × 22/7 × r.h = 264

➥ r.h = 264 × 7 /(2×22)

➥ r.h = 12 × 7/2

➥r.h = 6 × 7

➥ h = 42/r

Now,

➥ Volume of cylindrical pillar = πr²h

➥ 924 = π.r²h

keep value of π & h

➥ 924 = 22/7 × r² × (42/r)

➥ 924 = 22 × 6 × r

➥ r = 924/(22 × 6 )

➥ r = 42 /6

➥ r = 7

Hence

• Radius of cylindrical pillar = 7 m

So,

• Diameter will be = 2 × r = 2 × 7 = 14 m

And,

• Height of cylindrical pillar will be (h) = 42/r = 42/7 = 6 m.

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