Question

6. The curved surface area of a cylindrical pillar is 264 m square and its volume is 924 m square.find the diameter and height of the pillar.
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Answer 1

$\large \dag$ Question :-

The curved surface area of a cylindrical pillar is 264 m square and its volume is 924 m square.find the diameter and height of the pillar.

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{Diameter \: of \:  piller\:  is \:14 \: m }} }$

$\red\dashrightarrow\underline{\underline{\sf  \green{Height \: of \:  piller\:  is \:6 \: m }} }$

$\large \dag$ Step by step Explanation :-

❒ We know that curved surface area of cylinder is :-

$\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{   \blue{CSA = 2\pmb\pi{r}^{}h \:  \:  \: }}}}$

where

• r = Radius of base of Cylinder

• h = Height of Cylinder

Now here in the question we have,

• CSA = 264 m²

⏩ Putting Value in formula ;

$:\longmapsto \rm 264 = 2\pi rh$

$:\longmapsto \rm\pi rh =\cancel \frac{264}{2}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf \pmb\pi rh = 132} }}}----(1)$

❒ Also we know that volume of cylinder is :-

$\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{   \blue{Volume = \pmb\pi{r}^{2}h \:  \:  \: }}}}$

where

• r = Radius of base of Cylinder

• h = Height of Cylinder

Now here in the question we have,

• Volume = 924 m³

⏩ Putting Value in formula ;

$:\longmapsto \rm 924 = \pi {r}^{2} h$

$:\longmapsto \rm 924 = (\pi rh).r$

✧ Putting Value of $\large \pmb{\sf\pi rh}$

$:\longmapsto \rm 924 = 132 \times r$

$:\longmapsto \rm r = \cancel\frac{924}{132}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf r = 7 \: m} }}}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{Radius \: of \: Piller = 7 \: m}}}}}$

$\therefore\rm Diameter = 2 \times Radius$

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{Diameter \: of \: Piller = 14 \: m}}}}}$

⏩ Putting Value of r in in eq (1) :-

$:\longmapsto \rm \pi \times 7 \times h = 132$

$:\longmapsto \rm \frac{22}{ \cancel7} \times \cancel 7 \times h = 132$

$:\longmapsto \rm h = \cancel \frac{132}{22}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf h= 6 \: m} }}}$

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{\text Height \: of \: Piller =6\: m}}}}}$

Answer 2

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

Need to Find : The diameter and height of the pillar

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★ Cᴏɴᴄᴇᴘᴛ :

According to the question, the curved surface area of the pillar is 264 m² and it's volume is 924 m³. Now, for the curved surface area we need to apply it's formula and get the height. After which using the volume of cylinder formula we can get the radius. From there we need to get the height and then finding the value of diameter.

★ Sᴏʟᴜᴛɪᴏɴ :

As we know that :

❍ Curved Surface Area = 2πrh ❍

➻ 264 = 2πrh

➻ 264 = 2(22/7) × r × h

➻ 264 = 44/7 × rh

➻ 264 × 7/44 = rh

➻ 42 = rh

➻ h = 42/r ... eq(1)

Now, getting the volume of cylinder

❍ Volume of Cylinder = πr²h ❍

➻ 924 = πr²h

➻ 924 = 22/7 × (r)² × 42/r

➻ 924 = 22/7 × r² × 42/r

➻ 924 = 22 × 6r

➻ 924 = 142r

➻ r = 924/142

➻ r = 7 m

Putting the value of radius to get the height and diameter

Height :

☞ Height = 42/r [from eq(1)]

☞ Height = 42/7

☞ Height = 6 m

Diameter :

☞ Diameter = 2(radius)

☞ Diameter = 2(7)

☞ Diameter = 14 m

• Henceforth, Height is 6m and the Diameter is 14m

★ Lᴇᴀʀɴ Mᴏʀᴇ :

• Perimeter of square = 4(side)
• Area of square = (side)²
• Perimeter of Rectangle = 2(L + B)
• Area of Rectangle = L × B
• Perimeter of circle = 2πr
• Area of Circle = πr²
• Perimeter of rhombus = 4(side)
• Area of rhombus = ½ × d₁ × d₂
• Perimeter of equilateral ∆ = 3(side)
• Area of equilateral ∆ = √¾(side)²

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