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

## 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 \(\begin{align}{m^2} \end{align}\).

## 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 \(\rm{Rs}\, 68.75\)