Along a highway 50conical pillars are constructed. Each pillar has base diameter 28 cm and vertical height 18cm. find the total cost of painting these pillars at the rate of Rs. 120 per m2
Answers
Given :- Along a highway 50conical pillars are constructed. Each pillar has base diameter 28 cm and vertical height 18cm. find the total cost of painting these pillars at the rate of Rs. 120 per m².
Solution :-
we know that,
- Slant height of cone = √[radius² + height²]
- CSA of cone = π * radius * slant height .
- Radius = diameter / 2 .
So,
→ Radius of cone = 28/2 = 14 cm.
then,
→ slant height of cone = √[14² + 18²] = √[196 + 324] = √(520) = 2√130 cm.
therefore,
→ curved surface area of one conical pillar = (22/7) * 14 * (2√130) = 22 * 2 * 2√130 = 88√130 cm².
hence,
→ curved surface area of 50 conical pillar = 50 * 88 * 11.40 = 50160 cm².
now, we know that,
- 10000 cm² = 1m².
then,
→ 10000 cm² = 1m².
→ 1 cm² = (1/10000) m²
→ 50160 cm² = (1/10000) * 50160 = 5.016 m²
hence,
→ total cost of painting these pillars at the rate of Rs. 120 per m² = 120 * 5.016 = Rs.601.92 (Ans.)
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Answer:
Step-by-step explanation:
given radius = 14cm and height = 18cm
curved surface area of cylinder = 2 π r h
= 2* 22/7* 14* 18 = 1584 sq. cm
= 1584/10000 sq. m
now C.S.A. of 50 such pillars = 1584/10000 * 50 = 7.92 sq. m
cost of painting 1 pillar = Rs.120
cost of painting 100 such pillars = 7.92 * 120
= Rs. 950.40--------------Ans