Question about Spatial Geometry: Metric Relations of Cones
Subject Mathematics
Mathematics
Source Originais Teachy
Originais Teachy
Topic Spatial Geometry: Metric Relations of Cones
Spatial Geometry: Metric Relations of Cones
Difficulty Hard
Hard
(Originais Teachy 2024) - Question Hard of Mathematics
A packaging company wants to create a new cardboard cone for storing food. They have specified that the volume of the cone should be exactly 1000 cm³ and that material economy suggests that the sum of the length of its generatrix with the height should be minimized. Based on this context, consider that the cone is formed from a circular sector of a circle with a radius of 10 cm and central angle α. (a) Determine the metric relationship that minimizes the sum of the generatrix with the height of the cone, relating α to these measures. (b) Calculate the minimum value of the sum of the generatrix with the height and discuss if this configuration is practical for the company in terms of manufacturing.Answer sheet:
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Curabitur id consequat justo. Cras pellentesque urna ante, eget gravida quam pretium ut. Praesent aliquam nibh faucibus ligula placerat, eget pulvinar velit gravida. Nam sollicitudin pretium elit a feugiat. Vestibulum pharetra, sem quis tempor volutpat, magna diam tincidunt enim, in ullamcorper tellus nibh vitae turpis. In egestas convallis ultrices. Sed non sem ultricies, sollicitudin sem facilisis, commodo justo. Maecenas mattis sodales nunc, et auctor massa fermentum a. Maecenas eget nisl felis.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Curabitur id consequat justo. Cras pellentesque urna ante, eget gravida quam pretium ut. Praesent aliquam nibh faucibus ligula placerat, eget pulvinar velit gravida. Nam sollicitudin pretium elit a feugiat. Vestibulum pharetra, sem quis tempor volutpat, magna diam tincidunt enim, in ullamcorper tellus nibh vitae turpis. In egestas convallis ultrices.
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