A bus stop is barricaded from the remaining part of the road,

Question:

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?

 

Solution:

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

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