Question

the pillars of a building are in the shape of cylinder of a diameter 48 cm and height 7m find the cost of painting 15 such pillars at a ratio of ₹5 per square metre​

Answer 1

Given :

• Diameter of cylinder = 48 cm
• Height of cylinder = 7 m

To Find :

• The cost of the painting if the rate is Rs. 5 per m² = ?

Solution :

★ First of all we will find the radius of cylinder :

⇒Radius of cylinder = Diameter of cylinder ÷ 2

⇒Radius of cylinder = 48 ÷ 2

⇒Radius of cylinder = 24 cm

• Hence,the radius of cylinder is 24 cm.

★ Converting height of cylinder from m to cm :

→ Height of cylinder = 7 m

→ Height of cylinder = 7 × 100

→ Height of cylinder = 700 cm

• Hence,height of cylinder is 700 cm.

★ Finding lateral surface area of cylinder :

⟶ CSA of cylinder = 2πrh

⟶ CSA of cylinder = 2 × 22/7 × 24 × 700

⟶ CSA of cylinder = 2 × 22 × 24 × 100

⟶ CSA of cylinder = 44 × 2400

⟶ CSA of cylinder = 105600 cm²

• Hence,the lateral surface area of cylinder is 105600 cm².

★ Finding lateral surface area of 15 cylindrical pillars :

➻ CSA of 15 cylinder = 15 × 2πrh

➻ CSA of 15 cylinder = 15 × 105600

➻ CSA of 15 cylinder = 1584000 cm²

• Hence,the lateral surface area of 15 cylinder is 1584000 cm².

★ Convert 1584000 cm² to m² :

➝ CSA of 15 cylinder = 1584000 cm²

➝ CSA of 15 cylinder = 1584000 ÷ (100 × 100)

➝ CSA of 15 cylinder = 1584000 ÷ 10000

➝ CSA of 15 cylinder = 158.4 m²

• Hence,the lateral surface area of 15 cylinder is 158.4 m².

★ Now,let's calculate the rate of painting on 1584000 cm² :

➺ Total cost of painting = 158.4 × 5

➺ Total cost of painting = Rs. 792

• Hence,The cost of the painting if the rate is Rs. 5 per m² is Rs. 792.

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large\underline{\green{\bf Given :-}}$

$\:\:$

• Pillars of a building are in the shape of cylinder

$\:\:$

• Diameter of cylinder = 48 cm

$\:\:$

• Height of cylinder = 7 m

$\:\:$

• Rate of painting is ₹5 per square metre

$\:\:$

$\large\underline{\red{\bf To \: Find :-}}$

$\:\:$

• The cost of painting 15 such pillars

$\:\:$

$\large\underline{\orange{\bf Solution :-}}$

$\:\:$

$\underline{\bold{\texttt{Lateral surface area of cylinder :}}}$

$\:\:$

➠ 2πrh ⚊⚊⚊⚊ ⓵

$\:\:$

Where,

$\:\:$

• r = Radius of cylinder

• h = Height of cylinder

$\:\:$

$\underline{\bold{\texttt{Lateral surface area of given cylindrical pillar :}}}$

$\:\:$

➜ $\sf r = \dfrac { D } { 2 }$

$\:\:$

Where ,

$\:\:$

• D = Diameter = 48 cm

$\:\:$

So,

$\:\:$

➜ $\sf r = \dfrac { 48} { 2 }$

$\:\:$

➠ r = 24 cm

$\:\:$

$\sf \boxed { 1 \: cm \: = \dfrac { 1 } { 100 } \: m }$

$\:\:$

$\sf \boxed { r \: = 24 \: cm \: = 0.24 \: m }$

$\:\:$

• r = 0.24 m

• h = 7 m

$\:\:$

⟮ Puting these values in ⓵ ⟯

$\:\:$

➜ 2πrh

$\:\:$

➜ $\sf 2 × \dfrac { 22 } { \cancel 7 } × 0.24 × \cancel 7$

$\:\:$

➜ 2 × 22 × 0.24

$\:\:$

➨ 10.56 sq. m.

$\:\:$

• Hence lateral surface area of 1 cylindrical pillar is 10.56 sq. m.

$\:\:$

$\underline{\bold{\texttt{Lateral surface area of 15 such pillars :}}}$

$\:\:$

➜ 15 × 10.56

$\:\:$

➨ 158.4 sq. m.

$\:\:$

• Hence the lateral surface area of 15 cylindrical pillars is 158.4 sq. m.

$\:\:$

$\underline{\bold{\texttt{Cost of painting of 15 pillars :}}}$

$\:\:$

Rate × Lateral surface area

$\:\:$

➜ 5 × 158.4

$\:\:$

➨ Rs 792

$\:\:$

• Hence the cost of painting of 15 cylindrical pillars is Rs 792

$\:\:$

━━━━━━━━━━━━━━━━━━━━━━━━━

$\:\:$

Additional information

$\:\:$

Total surface area of cylinder

$\:\:$

• 2πr(r + h)

$\:\:$

Where,

$\:\:$

➻ r = Radius

➻ h = Height

$\:\:$

Volume of cylinder

$\:\:$

• πr² h

$\:\:$

Where,

$\:\:$

➻ r = Radius

➻ h = Height

═════════════════════════