A bus stop is barricaded from the remaining part of the road, by using 50 hollow cone made of recycled card-board. 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 Rs. 12 per m2. What will be the cost of painting all these cones. (Use π=3.14 and√1.04 = 1.02).
Answers
the cost of painting 50 cones = Rs 384.34
Step-by-step explanation:
Each cone has a base diameter of 40 cm and height 1 m
=> Radius = Diameter/2 = 40/2 = 20 cm = 0.2 m
height = 1 m
Lateral height = √1² + 0.2² = √1 + 0.04 = √1.04 = 1.02 m
Lateral surface area = π r L
= 3.14 * 0.2 * 1.02 m²
Area of 50 cones = 50 * 3.14 * 0.2 * 1.02 m²
= 10 * 3.14 * 1.02 m²
= 32.028 m²
cost of painting is Rs. 12 per m²
Total Cost of Painting = 12 * 32.028
= 384.336
= 384.34 Rs
the cost of painting all these cones = Rs 384.34
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Radius of the cone (r) = 40/2 cm = 20 cm = 0.2 m
Height of the cone (h) = 1 m
Let l be the slant height of a cone.
∴ l = √h2 + r2
⇒ l = √12 + 0.22
⇒ l = √1.04
⇒ l = 1.02 m
Rate of painting = ₹12 per m2
Curved surface of 1 cone = πrl m2
= (3.14 × 0.2 × 1.02) m2
= 0.64056 m2
Curved surface of such 50 cones = (50 × 0.64056) m2
= 32.028 m2
Cost of painting all these cones = ₹(32.028 × 12)
= ₹384.34