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Question
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 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is ₹ 12 per m2, what will be the cost of painting all these cones?
`("Use "π = 3.14" and take "sqrt1.04= 1.02)`
Solution
The diameter of the base = 40 cm
∴ Radius (r) = `40/2 cm` = 20 cm = `20/100 m` = 0.2 m
Height (h) = 1 m
∴ Slant height(l) = `sqrt(r^2 + h^2)`
= `sqrt((0.2)^2 + (1)^2) m`
= `sqrt(0.04 + 1) m`
= `sqrt(1.04) m`
= 1.02 ...`sqrt1.04` = 1.02 (given)
Now, curved surface area = πrl
∴ The curved surface area of a cone
= 3.14 × 0.2 × 1.02 m2
= `314/100 xx 2/10 xx 102/100 m^2`
⇒ Curved surface area of 50 cones
= `50 xx [314/100 xx 2/10 xx 102/100] m^2`
= `(314 xx 102)/(10 xx 100) m^2`
Cost of painting 1 m2 area = ₹ 12
∴ Total cost of painting `[(314 xx 102)/1000] m^2` area
= ₹ `((12 xx 314 xx 102)/1000)`
= ₹ `384336/1000`
= ₹ 384.336
= ₹ 384.34 (approx.)
Thus, the required cost of painting is ₹ 384.34 (approx.).
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