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Evaluating triple integrals: Each of the triple integrals that follows represents the volume of a solid. Sketch the solid and evaluate the integral.

0π020rsinθrdzdrdθ

Short Answer

Expert verified

0π020rsinθrdzdrdθ=163

Step by step solution

01

Given

We have to find the volume by using the triple integral.

0π020rsinθrdzdrdθ
02

Evaluate the integral

V=0π020rsinθrdzdrdθV=0π02rrsinθ-0drdθV=0π02r2sinθdrdθV=0πsinθdθ02r2drV=0πsinθdθr3302V=830πsinθdθV=83-cosθ0πV=83-cosπ+cos0V=831+1V=163cubicunits

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