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Ex.13.2 Q5 Surface Areas and Volumes - NCERT Maths Class 9

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Question

A cylindrical pillar is \(50\,\rm{ cm}\) in diameter and \(3.5\,\rm{ m}\) in height. Find the cost of painting the curved surface of the pillar at the rate of \(\rm{Rs}\, 12.50\) per \(\begin{align}{m^2} \end{align}\).

 Video Solution
Surface Areas And Volumes
Ex 13.2 | Question 5

Text Solution

Reasoning:

The curved surface area of a right circular cylinder of base radius \(r\) and height \(h\) is \(\begin{align}2\pi rh \end{align}\). So, the cost of painting curved surface area will be the product of curved surface are and cost of painting per meter square.

What is the known?

Height and diameter of the pillar.

What is the unknown?

Cost of painting the curved surface of the pillar.

Steps:

Diameter = \(2r\) = \(50\,\rm{ cm}\)

\(r\) = \(25\,\rm{ cm}\) = \(0.25\,\rm{ cm}\)

Height = \(h\) = \(3.5\,\rm{ m}\)

Curved surface area 

\[\begin{align}&= {2\pi rh }\\ &= 2 \times \frac{{22}}{7} \times 0.25 \times 3.5\\ &= 5.5\,\,\rm{{m^2}} \end{align}\]

Cost of painting the curved surface area per

\(\begin{align}\rm{{m^2}} \end{align}\)= \(\rm{Rs}\, 12.50.\)

Cost of painting

\(\begin{align}\,5.5\,\,\rm{{m^2}} = 12.50 \times 5.5\,\, = Rs\,\,68.75 \end{align}\)

Cost of painting the curved surface of the pillar is \(\rm{Rs}\, 68.75\)