A right square frustum has upper and lower base edges of lengths 2 and 4 respectively, and lateral edge length 2. Its volume is A. $20 + 12 \sqrt { 3 }$ B. $28 \sqrt { 2 }$ C. $\frac { 56 } { 3 }$ D. $\frac { 28 \sqrt { 2 } } { 3 }$
D The height of the frustum is $h = \sqrt { 2 ^ { 2 } - ( 2 \sqrt { 2 } - \sqrt { 2 } ) ^ { 2 } } = \sqrt { 2 }$. The lower base area is $S _ { 1 } = 16$, and the upper base area is $S _ { 2 } = 4$. Therefore, the volume of the frustum is $V = \frac { 1 } { 3 } h \left( S _ { 1 } + S _ { 2 } + \sqrt { S _ { 1 } S _ { 2 } } \right) = \frac { 1 } { 3 } \times \sqrt { 2 } \times ( 16 + 4 + \sqrt { 64 } ) = \frac { 28 } { 3 } \sqrt { 2 }$.
A right square frustum has upper and lower base edges of lengths 2 and 4 respectively, and lateral edge length 2. Its volume is
A. $20 + 12 \sqrt { 3 }$
B. $28 \sqrt { 2 }$
C. $\frac { 56 } { 3 }$
D. $\frac { 28 \sqrt { 2 } } { 3 }$