Use a double integral to find the volume of the solid shown in the figure.
A) 5,996
B) 5,994
C) 6,000
D) 6,008

Name: Use a double integral to find the volume of the solid shown in the figure. A) 5,996 B) 5,994 C) 6,000 D) 6,008
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Question

Use a double integral to find the volume of the solid shown in the figure. 
A) 5,996 
B) 5,994 
C) 6,000 
D) 6,008

Quizplus · Accepted Answer

We can set up the double integral in the xy-plane as follows:
$$\int_{-3}^{3}\int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}}(6-x^2-y^2)dydx$$
Evaluating this integral gives us a volume of 6,000, so the answer is (C).

Use a Double Integral to Find the Volume of the Solid