A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled card board. Each cone has a base diameter of $40 \mathrm{~cm}_{2}$ 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?
The area to be painted is the curved surface area of each cone.
The formula of the curved surface area of a cone with base radius and slant height 7 is given as
Curved Surface Area = πrl
For each cone, we're given that the base diameter is 0.40 m.
$\mathrm{l}=\sqrt{\mathrm{r}^{2}+\mathrm{h}^{2}}$
$=\sqrt{0.2^{2}+1^{2}}$
$=\sqrt{0.04+1}$
$=\sqrt{1.04}$
l = 1.02 m
Now substituting the values of r = 0.2 m and slant height 1= 1.02 m and using pi = 3.14 in the formula of C.S.A.
We get Curved Surface Area $=(3.14)(0.2)(1.02)=0.64056 \mathrm{~m}^{2}$
This is the curved surface area of a single cone.
Since we need to paint 50 such cones the total area to be painted is,
Total area to be painted $=(0.64056)(50)=32.028 \mathrm{~m}^{2}$
The cost of painting is given as Rs. 12 per $\mathrm{m}^{2}$
Hence the total cost of painting = (12) (32.028) = 384.336
Hence, the total cost that would be incurred in the painting is Rs. 384.336