# Ex.13.3 Q6 Surface Areas and Volumes Solution - NCERT Maths Class 9

## Question

The slant height and base diameter of a conical tomb are \(25\rm\, m\) and \(14\rm\, m\) respectively. Find the cost of white washing its curved surface at the rate of \( \rm\,Rs \,210\) per \(100\) \(\rm\,{m^2} \).

## Text Solution

**Reasoning:**

Curved surface area of a right circular cone of \(r\) base radius and slant height is \(\pi rl \).

**What is known?**

Slant height and base diameter rate of white washing \(\rm Rs\, 210\) per \(100\)\(\begin{align}\rm\,{m^2} \end{align}\).

**What is unknown?**

Cost of white washing its curved surface area.

**Steps:**

Slant Height \((l) = 25\rm\, m\)

\[\begin{align}r = \frac{{14}}{2} = 7\rm\,m \end{align}\]

Curved surface area \(\begin{align} = \pi rl \end{align}\)

\[\begin{align} &= \frac{{22}}{7} \times 7 \times 25\\&=550\rm\,\,{m^2} \end{align}\]

Cost of white washing per \(\begin{align}100\rm\,\,{m^2} \end{align}\) \(= 210\)

\[\begin{align}{\rm{For}}\,\,550\rm\,\,{m^2} &= \frac{{210 \times 550}}{{100}}\\ &= {\rm{ Rs }}\,1155 \end{align}\]

**Answer:**

Cost of white washing the conical tomb is \(\rm Rs.\, 1155.\)