# Ex.13.3 Q8 Surface Areas and Volumes Solution - NCERT Maths Class 9

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## Question

A bus stop is barricaded from the remaining part of the road, by using $$50$$ hollow cones made of recycled cardboard. Each cone has a base diameter of $$40\rm\, cm$$ and height $$1\rm\, m.$$ If the outer side of each of the cones is to be painted and the cost of painting is $$\rm Rs\, 12$$ per $$\rm m^{2}$$ . What will be the cost of painting all these cones?

(Use $$\pi = 3.14$$ and take $$\sqrt{1.04}= 1.02$$)

Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-3 | Question 8

## Text Solution

Reasoning:

Curved surface area of a right circular cone of base radius $$r$$ and slant height l is $$= \pi rl$$ and $$l = \sqrt {{r^2} + {h^2}}$$

What is known?

Base diameter and height of the cone number of cones and cost per $$\rm\,{m^2}.$$

What is unknown?

Cost of painting the $$50$$ cones.

Steps:

\begin{align} \text{Base diameter} &=40 {\rm{cm}}\\2r & =40 {\rm{cm}} \\ r &= \frac{{40}}{2} \\ &= 20\,\,{\rm{cm}}\\ & = 0.2 \, {\rm{m}}\; \begin{bmatrix} \because 100\,{\rm{cm}} \\ = 1\,{\rm{m}}\end{bmatrix} \end{align}

Height $$h = 1\rm\, m$$

\begin{align}l &= \sqrt {{r^2} + {h^2}} \\ &= \sqrt {{{(0.2)}^2} + {{(1)}^2}} \\ &= \sqrt {1.04} \\ &= 1.02\rm \,m \end{align}

Curved surface are $$=$$ \begin{align}\pi rl \end{align}

\begin{align} &= \pi \times 0.2 \times 1.02\\ &= 3.14 \times 0.2 \times 1.02\\ &= 0.64056\,\,\rm\,{m^2} \end{align}

Curved surface area of $$50$$ cones

\begin{align} &= 0.64056 \times 50\\ &= 32.028\,\,\rm{m^2} \end{align}

Cost of painting per \begin{align}\rm{m^2} \end{align} $$=\rm Rs\, 12$$

Cost of painting $$32.028\rm\,{m^2}$$

\begin{align} &= \rm Rs\,\,32.028 \times 12 \\ &= \rm Rs\,\,\,\,384.34\,\,\rm\,{m^2} \end{align}

$$=\rm Rs\, 384.34$$