Standard #: MAFS.912.C.5.7 (Archived Standard)


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Use definite integrals to find the volume of a solid with known cross-sectional area, including solids of revolution.


Remarks


Example 1: A cone with its vertex at the origin lies symmetrically along the x-axis. The base of the cone is at x = 5 and the base radius is 7. Use integration to find the volume of the cone.

Example 2: What is the volume of the solid created when the area between the curves f(x) = x and g(x) = x2  for 0 ≤ x ≤ 1 is revolved around the y-axis?

General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Calculus
Cluster: Applications of Integration - Apply knowledge about integrals to finding velocities from accelerations, solving separable differential equations, and finding areas and volumes. Apply integration to model, and solve problems in physics, biology, economics, etc. Find velocity functions and position functions from their derivatives, solve separable differential equations, and use definite integrals to find areas and volumes.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived

Related Courses

Course Number1111 Course Title222
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))


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