At What Rate Is the Diagonal of a Cube Increasing $\sqrt { 3 } \mathrm { in } / \mathrm { min }$

At what rate is the diagonal of a cube increasing if its edges are 2 inches and are increasing at a rate 3 inches per minute?

A) $\sqrt { 3 } \mathrm { in } / \mathrm { min }$

B) $6 \sqrt { 3 } \text { in } / \min$
C) $2 \sqrt { 3 } \mathrm { in } / \mathrm { min }$
D) $72 \text { in } / \mathrm { min }$
E) $3 \sqrt { 3 } \text { in } / \min$
F) $9 \mathrm { in } / \mathrm { min }$

G) $36 \text { in } / \mathrm { min }$

H) $24 \text { in } / \mathrm { min }$

Correct Answer:

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