Question

You work as a purchasing agent at a manufacturing facility that makes right circular cones. The best price you find for the aluminum used to make the cones is $0.009 per square inch. If a cone has a radius of 1.65 inches and a height of 4.60 inches, what is the cost to produce 75 cones?

Answer 1

Solution :

Formula for surface area of a right circular cone is : Lateral Surface area (LSA)=π x r x l

where, r= radius and l = slant height

Slant height can be calculated as : Slant height l=sqrt h^2 + r^2

l=sqrt 1.65^2 + 4.6^2 = sqrt 21.16 + 2.7225 = sqrt 23.8825 = 4.89 inches

Therefore, SLA = 3.14 x 1.65 x 4.89 = 25.34 sq inches

Base area (BA) = π r^2 = 3.14 x 1.65^2 = 8.55 sq. inches

Total surface are of cone = Base Area + Lateral surface area = 8.55 + 25.34 = 33.89 sq. inches

For 75 cones we will need : 75 x 33.89 = 2541.75 sq inches of Aluminium

Price of Aluminium is $0.009 per sq. inch

Therefore cost of 2541.75 sq inches of Aluminium = 2541.75 x 0.009 = $22.86

ANSWER : Cost to produce 75 cones is $ 22.86

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