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)`

Answer 1

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.).