Solve the Problem $\varrho = 10$ In Rectangular Coordinates B) C) $8 \int_{-10}^{10} \int_{0}^{\sqrt{100-x^{2}}} \int_{0}^{\sqrt{100-x^{2}-y^{2}}} d z d y d x$

question 139

Multiple Choice

Solve the problem.
-Set up the triple integral for the volume of the sphere $\varrho = 10$ in rectangular coordinates.

• A) \(8 \int _ { - 10 } ^ { 10 } \int _ { - \sqrt { 100 - x ^ { 2 } } } ^ { \sqrt { 100 - x ^ { 2 } } } \int _ { 0 } ^ { \sqrt { 100 - x ^ { 2 } - y ^ { 2 } } } d z d y d x\)
• B) \(\int _ { 0 } ^ { 10 } \int _ { - \sqrt { 100 - x ^ { 2 } } } ^ { \sqrt { 100 - x ^ { 2 } } } \int _ { - \sqrt { 100 - x ^ { 2 } - y ^ { 2 } } } ^ { \sqrt { 100 - x ^ { 2 } - y ^ { 2 } } } d z d y d x\)
• C)\(8 \int_{-10}^{10} \int_{0}^{\sqrt{100-x^{2}}} \int_{0}^{\sqrt{100-x^{2}-y^{2}}} d z d y d x\)
• D)
• \(\int_{-10}^{10} \int_{-\sqrt{100-x^{2}}}^{\sqrt{100-x^{2}}} \int \sqrt{100-x^{2}-y^{2}} d z d y d x\)

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