Use a Double Integral in Polar Coordinates to Find the Volume

question 90

Multiple Choice

Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere $z = \sqrt { 64 - x ^ { 2 } - y ^ { 2 } }$ but outside the cylinder $x ^ { 2 } + y ^ { 2 } = 25$

• A) \(\frac { 2 } { 3 } 39 ^ { 3 / 2 }\)
• B) \(\frac { 2 } { 3 } 39 ^ { 3 / 2 } \pi\)
• C) \(\frac { 4 } { 3 } 39 ^ { 3 / 2 } \pi\)
• D) \(\frac { 2 } { 3 } 39 ^ { 1 / 2 } \pi\)
• E) \(\frac { 3 } { 2 } 39 ^ { 3 / 2 }\)