The volume of the solid in the first octant bounded by and all the coordinate planes is

A) $\frac { 4 ( 9 \sqrt { 5 } + 2 \pi ) } { 3 }$
B) $\frac { 4 ( 9 \sqrt { 3 } - 2 \pi ) } { 5 }$
C) $\frac { 4 ( 9 \sqrt { 3 } + 2 \pi ) } { 3 }$
D) $\frac { 4 ( 9 \sqrt { 3 } - 2 \pi ) } { 3 }$
E) $\frac { 4 ( 9 \sqrt { 3 } + 2 \pi ) } { 5 }$

Question

The volume of the solid in the first octant bounded by and all the coordinate planes is

A) $\frac { 4 ( 9 \sqrt { 5 } + 2 \pi ) } { 3 }$
B) $\frac { 4 ( 9 \sqrt { 3 } - 2 \pi ) } { 5 }$
C) $\frac { 4 ( 9 \sqrt { 3 } + 2 \pi ) } { 3 }$
D) $\frac { 4 ( 9 \sqrt { 3 } - 2 \pi ) } { 3 }$
E) $\frac { 4 ( 9 \sqrt { 3 } + 2 \pi ) } { 5 }$

Quizplus · Accepted Answer

The solid is a cone with radius 3 and height 3. The volume of a cone is $\frac { 1 } { 3 } \pi r ^ { 2 } h$, so the volume of this cone is $\frac { 1 } { 3 } \pi ( 3 ) ^ { 2 } ( 3 ) = 9 \pi$. The volume of the solid in the first octant is one-eighth of this, or $\frac { 9 \pi } { 8 } = \frac { 4 ( 9 \sqrt { 3 } + 2 \pi ) } { 3 }$.

The Volume of the Solid in the First Octant Bounded 4(95+2π)3\frac { 4 ( 9 \sqrt { 5 } + 2 \pi ) } { 3 }34(95​+2π)​

The Volume of the Solid in the First Octant Bounded $\frac { 4 ( 9 \sqrt { 5 } + 2 \pi ) } { 3 }$