Question

A cylindrical vessel open at the top has a base radius of 28 cm. if the total cost of painting the outer part of the vessel is RS. 357 at the rate of 0.2 per 100cm^2 . Then the height of the vessel is.......​

Answer 1

$\underline{\underline{\sf{\color{red}{GIVEN:-}}}}$

A cylindrical vessel open at the top has a base radius of 28 cm. The total cost of painting the outer part of the vessel is ₹ 357 at the rate of ₹ 0.2 per 100 cm².

• Radius, r = 28 cm
• Cost of painting the outer part of the vessel = ₹ 357
• Cost of painting 100 cm² of area = ₹ 0.2

$\underline{\underline{\sf{\color{red}{TO\ FIND:-}}}}$

The height, h of the vessel.

$\underline{\underline{\sf{\color{red}{SOLUTION:-}}}}$

For ₹ 0.2, 100 cm² of area is painted.

For ₹ 1,

100/0.2 = 500 cm² of area is painted.

For ₹ 357,

357 × 500 = 178500 cm² of area is painted.

A/q,

◘ 178500 cm² is the CSA of the cylindrical vessel.

_________________

We know,

$\boxed{\bf{\dag\ CSA=2 \pi rh}}$

Substituting the values :-

$\sf{178500=2 \pi (28)h}$

$\sf{\longrightarrow 178500=2 \times \dfrac{22}{7} \times 28 \times h }$

$\sf{\longrightarrow 178500=44\times4\times h}$

$\sf{\longrightarrow h=\dfrac{178500}{176} }$

$\sf{\longrightarrow h=1014.2\ cm}$

$\sf{\longrightarrow h=10.14\ m}$

Answer 2

Given :

• A cylindrical vessel is open at the top
• Base radius of Cylinder, r = 28 cm
• Total cost of painting the outer part of the vessel is Rs. 357  at the rate of 0.2 per 100 cm²

To find :

• Height of the cylindrical vessel, h =?

Formula required :

• Formula for CSA of cylinder

     CSA of cylinder = 2 π r h

• Formula for area of circular base of cylinder

   Area of circular base = π r²

[ Where r is base radius of cylinder and h is height of cylinder ]

Solution :

Total cost given for painting the vessel = Rs. 357

Rate of painting = Rs. 0.2 per 100 cm²

so,

→ CSA of cylinder + area of base of cylinder = ( 357 ) / ( 0.2 / 100 )

→  CSA of cylinder + area of base of cylinder = ( 357 ) × 1000 / 2

→ CSA of cylinder + area of base of cylinder = 178500 cm²

That is,

→ 2 π r h + π r² = 178500 cm²

→ [ 2 × (22/7) × 28 × h ] + [ (22/7) × (28)² ] = 178500

→ 176  h + 2464 = 178500

→ 176  h = 178500 - 2464

→ 176 h = 176036

→ h = 176036 / 176

→ h = 1000.20455  cm

→ h = 10 m (approx.)

Therefore,

• Height of the vessel would be 10 metres. (approx.)