A bus stop is barricated from the remaining part of the road by using 50 hollow cones made of recycled cardboard.
Question:

A bus stop is barricated from the remaining part of the road by using 50 hollow cones made of recycled cardboard. Each one 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 $₹ 25$ per $\mathrm{m}^{2}$, what will be the cost of painting all these cones? (Use $\pi=3.14$ and $\sqrt{1.04}=1.02$ ).

Solution:

Radius of each cone, $r=\frac{40}{2}=20 \mathrm{~cm}=0.2 \mathrm{~m} \quad(1 \mathrm{~m}=100 \mathrm{~cm})$

Height of each cone, h = 1 m

$\therefore$ Slant height of each cone, $l=\sqrt{r^{2}+h^{2}}=\sqrt{(0.2)^{2}+1^{2}}=\sqrt{0.04+1}=\sqrt{1.04}=1.02 \mathrm{~m}$

Curved surface area of each cone $=\pi r l=3.14 \times 0.2 \times 1.02=0.64056 \mathrm{~m}^{2}$

$\therefore$ Curved surface area of 50 cones $=0.64056 \times 50=32.028 \mathrm{~m}^{2}$

Cost of painting = ₹ 25 per m2

∴ Total cost of painting all the cones

= Curved surface area of 50 cones × ₹ 25

= 32.028 × 25

= ₹ 800.70

Thus, the cost of painting all the cones is ₹ 800.70.

 

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