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 \(100\) \(\rm\,{m^2} \).

 Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-3 | Question 6

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 \(\rm Rs.\, 1155.\)

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