Question

Q.15)The curved surface area of the cylindrical pillar is 264m² and its volume is 924m³.find the height of pillar?

Answer 1

Given :

• CSA (curved surface area) of cylindrical pillar = 264 m²
• volume of cylindrical pillar = 924 m³

To find :

• height of the pillar, h = ?

Formula required :

• formula for CSA of cylinder

      2 π r h

• formula for Volume of cylinder

     π r² h

[ where r is radius and h is height of cylinder ]

Solution :

Let, height of cylinder be h and radius of cylinder be r

then,

• → CSA of cylinder = 264 m²

• → 2 π r h = 264
• → 2 (22/7) r h = 264
• → r h = 264 × 7 / 44
• → r h = 42
• → r = 42 / h  _____equation (1)

and,

• → Volume of cylinder = 924 m³

• → π r² h = 924
• → (22/7) r² h = 924
• → r² h = 924 * 7 / 22
• → r² h = 294

using equation (1)

• → (42/h)² h = 294
• → ( 1764 / h² ) h = 294
• → 1764 / h = 294
• → h = 1764 / 294
• → h = 6 m  

therefore,

Height of cylindrical pillar is 6 metres .  

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The curved surface area of cylindrical pillar = 264m²

• The Volume of the cylindrical pillar = 924m³

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The height of the cylindrical pillar.

$\bf{\underline{\underline\green{Solution:-}}}$

As we know that:-

The curved surface area(CSA) of cylindrical pillar is given by the formula:-

$\boxed{\rm \longrightarrow CSA \: of \: cylinder \: =2\pi rh }......(i)$

The Volume of the cylinder is given by the formula:-

$\boxed{\rm \longrightarrow Volume \: of \: cylinder \: =\pi {r}^{2} h }.....(ii)$

On dividing (ii) by (i)

$\rm\longrightarrow \dfrac{\pi {r}^{2} h}{2\pi rh} = \dfrac{924}{264}$

$\rm\longrightarrow \dfrac{ {r}}{2} = \dfrac{924}{264}$

$\rm\longrightarrow { {r}} = \dfrac{924 \times 2}{264}$

$\rm\longrightarrow { {r}} = 7m$

Substituting r = 7 in equation (i)

$\rm\longrightarrow 2\pi rh = 264$

$\rm\longrightarrow 2 \times \pi \times (7) \times h = 264$

$\rm\longrightarrow 2 \times \dfrac{22}{7} \times 7 \times h = 264$

$\rm\longrightarrow 2 \times \dfrac{22}{ \not7} \times \not7 \times h = 264$

$\rm\longrightarrow 2 \times {22} \times h = 264$

$\rm\longrightarrow44 \times h = 264$

$\rm\longrightarrow h = \dfrac{264}{44}$

$\rm\longrightarrow h = 6$

Therefore:-

$\underline{\boxed {\bf \purple{\rightarrow Height \: of \: the \: cylindrical \: pillar = 6m }}}$