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Volume of a conical slice

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20. R is a slice of thickness k perpendicular to the axis of a right circular cone having maximum radius b and minimum radius a. Show that its volume is V(R) = pi/3(a^2 + ab + b^2)k.

Explain how Exercise 18 and 19 are essentially special cases of this.

18. C is a cone of height h and base radius a. Show V(C) = pi/3*a^2*h.

19. L is a right circular cylinder a height k and radius a. Show V(L) = pi*a^2*k.

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Solution Summary

The 3-pages file contain a detailed solution, including graphics, that demonstrates how to utilize the solid of rotation integrals to find the volume of the sliced cone.

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