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 \mathrm{~cm} $ and height $ 1 \mathrm{~m} $. If the outer side of each of the cones is to be painted and the cost of painting is $ Rs.\ 12 $ per $ \mathrm{m}^{2} $, what will be the cost of painting all these cones? (Use $ \pi=3.14 $ and take $ \sqrt{1.04}=1.02) $.

 Given:

A bus stop is barricated from the remaining part of the road, by using $50$ hollow cones made of recycled card-board.

Each cone has a base diameter of $40\ cm$ and a height of $1\ m$.

The outer side of each of the cones is to be painted and the cost of painting is $Rs.\ 12$ per $m^2$.

To do:

We have to find the cost of painting these cones. 

Solution:

Diameter of the base of the tent $= 40\ cm$

This implies,

Radius of the base of the cone $(r) = \frac{40}{2}$

$=20 \mathrm{~cm}$

$=0.2 \mathrm{~m}$

Height of the cone $(h)=1 \mathrm{~m}$

$=100 \mathrm{~cm}$

Therefore,

Slant height of the cone $(l)=\sqrt{r^{2}+h^{2}}$

$=\sqrt{(20)^{2}+(100)^{2}}$

$=\sqrt{400+10000}$

$=\sqrt{10400} \mathrm{~cm}$

$=102 \mathrm{~cm}$

$=1.02 \mathrm{~m}$

The curved surface area of one cone $=\pi r l$

$=3.14 \times 0.2 \times 1.02$

$=0.64056 \mathrm{~m}^{2}$

The curved surface area of 50 such cones $=0.64056 \times 50$

$=32.028 \mathrm{~m}^{2}$

Rate of painting $= Rs.\ 12$ per $\mathrm{m}^{2}$

Total cost of painting $=Rs.\ 32.028 \times 12$

$=Rs.\ 384.336$

$=Rs.\ 384.34$

Hence,

The total cost of painting these cones is $Rs.\ 384.34$.

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Updated on: 10-Oct-2022

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