Answer:

Cost of painting the 50 hollow cones, if the cost of painting is Rs 12 m² is Rs 384.34

Step-by-step explanation:

Given that, a bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard.

Further given that, each cone has a base diameter of 40 cm and height 1 m.

So, we have

Height of cone, h = 1 m

Radius of cone, r = 20 cm = 0.2 m

We know, Slant height (l), height (h) and radius (r) is connected by a relationship

[tex] \sf \: {l}^{2} = {h}^{2} + {r}^{2} \\ [/tex]

[tex] \sf \: {l}^{2} = {(1)}^{2} + {(0.2)}^{2} \\ [/tex]

[tex] \sf \: {l}^{2} =1 + 0.04 \\ [/tex]

[tex] \sf \: {l}^{2} = 1.04 \\ [/tex]

[tex] \sf \: l = \sqrt{1.04} = \sqrt{ {(1.02)}^{2} } \\ [/tex]

[tex]\implies\sf\:l = 1.02 \: m \\ [/tex]

Thus, Slant height of a cone is 1.02 m

Now, Amount of paint required to to paint the 50 hollow cones is equals to 50 times the Curved Surface Area of cone.

Thus,

[tex] \sf \: Amount\:of\:paint\: required = 50\:\pi \: r \: l \\ [/tex]

[tex] \sf \: Amount\:of\:paint\: required = 50 \times 3.14 \times 0.2 \times 1.02\\ [/tex]

[tex] \implies\sf\: Amount\:of\:paint \: required = 32.028 \: {m}^{2} \\ [/tex]

Now, Further given that

[tex] \sf \: Cost\:of\: {1 \:m }^{2} \: of \: painting = Rs \: 12 \\ [/tex]

So,

[tex] \sf \: Cost\:of\:32.028 \: {m }^{2} \: of \: painting = 32.028 \times 12 \\ [/tex]

[tex]\implies\sf\: Cost\:of\:32.028 \: {m }^{2} \: of \: painting = Rs \: 384.34 \\ [/tex]

Hence, Cost of painting the 50 hollow cones, if the cost of painting is Rs 12 m² is Rs 384.34