Question

Find the cost of painting the total outside surface area of solid cylinder 20m in height and 50cm in diameter at $10.50 per square. m.

Answer 1

AnswEr :

• Height ( h ) = 20 m
• Diameter = 50 cm
• Radius ( r ) = $\rm\dfrac{50}{2}$ = 25 cm = 0.25 m

• we will calculate TSA of Cylinder now :

⇒ TSA of Cylinder = 2πr(r + h)

• plugging the values

⇒ TSA = 2 × $\rm\dfrac{22}{7}$ × 0.25 (0.25 + 20)

⇒ TSA = $\rm\dfrac{44}{7}$ × 0.25 × 20.25

⇒ TSA = $\sf\dfrac{222.75}{7}\:{m}^{2}$

• calculation of cost of painting now :

⇒ Cost = TSA × Rate

⇒ Cost = $\rm\dfrac{222.75}{7}$× 10.50

⇒ Cost = $\rm\dfrac{2338.875}{7}$

⇒ Cost = Rs. 334.12

⠀

∴ Cost of TSA of Cylinder is Rs. 334.12

Answer 2

Question :------- we have to find cost of Painting the Total outside surface area of solid cylinder ..

Given :------

• Height of cylinder = 20m
• Diameter =50cm
• cost of painting = $10.50 /m²

Formula to be used :-------

• Total outside surface area of solid cylinder = CSA of cylinder + Base Area of both ends = 2πrh + 2πr² = 2πr(h+r)
• 100 cm = 1m .......
• Radius = Diameter/2

Radius of cylinder is = 50/2 = 25 cm = 25/100 = 1/4 m

Putting values in Above formula we get,

Total outside surface Area =

$2\pi \times r(h + r) \\ \\ \implies \: 2 \times \frac{22}{7} \times \frac{1}{4}(20 + \frac{1}{4} ) \\ \\ \implies \: \frac{11}{7} \times \frac{81}{4} = 31.82 \: m^{2}$

Now,

it is given that , cost of painting for 1 m² Area is = $ 10.5

so,

cost of painting Total outside surface area

= 10.5 × 31.82 = $ 334.11 (Ans) ....

(Hope it Helps you)

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Volume of cylinder is = πr²h

CSA of cylinder is = 2πrh

Base Area of cylinder is = πr²

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