Question

What volume is equivalent to $14,000{\mathrm{mm}}^3$?

• A. $1.4x{10}^{-5}{\mathrm{m}}^3$
• B. $1.4x{10}^{-2}{\mathrm{m}}^3$
• C. $1.4x{10}^2{\mathrm{cm}}^3$
• D. $1.4x{10}^6{\mathrm{cm}}^3$

Answer 1

The correct option is A

$1.4x{10}^{-5}{\mathrm{m}}^3$

Which volume is equivalent to $14,000{\mathrm{mm}}^3$.

Determine the correct option.

Explanation of correct option:

Option (A):

Convert ${\mathrm{mm}}^3$ into ${\mathrm{m}}^3$.

Since $1{\mathrm{mm}}^3=1\times {10}^{-9}{\mathrm{m}}^3$.

Convert $14,000{\mathrm{mm}}^3$ into ${\mathrm{m}}^3$.

So,

$\begin{array}{rcl}14000{\mathrm{mm}}^3& =& 14000\left(1\times {10}^{-9}{\mathrm{m}}^3\right)\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14000\times {10}^{-9}{\mathrm{m}}^3\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14\times 1000\times {10}^{-9}{\mathrm{m}}^3\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14\times {10}^3\times {10}^{-9}{\mathrm{m}}^3\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14\times {10}^{3-9}{\mathrm{m}}^3\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14\times {10}^{-6}{\mathrm{m}}^3\\ \therefore 14000{\mathrm{mm}}^3& =& 1.4\times {10}^{-5}{\mathrm{m}}^3\end{array}$

Therefore, the volume $1.4\times {10}^{-5}{\mathrm{m}}^3$ is equivalent to $14,000{\mathrm{mm}}^3$.

Hence, Option (A) is correct.

Explanation of incorrect options:

Option (B):

The volume $1.4\times {10}^{-2}{\mathrm{m}}^3$ is not equivalent to $14,000{\mathrm{mm}}^3$.

Because the correct volume is $1.4\times {10}^{-5}{\mathrm{m}}^3$.

So, Option (B) is incorrect.

Option (C):

The volume $1.4\times {10}^2{\mathrm{cm}}^3$ is not equivalent to $14,000{\mathrm{mm}}^3$.

Since $1{\mathrm{mm}}^3=1\times {10}^{-3}{\mathrm{cm}}^3$.

Convert $14,000{\mathrm{mm}}^3$ into ${\mathrm{cm}}^3$.

So,

$\begin{array}{rcl}14000{\mathrm{mm}}^3& =& 14000\left(1\times {10}^{-3}c{\mathrm{m}}^3\right)\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14000\times {10}^{-3}c{\mathrm{m}}^3\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14\times 1000\times {10}^{-3}c{\mathrm{m}}^3\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14\times {10}^3\times {10}^{-3}{\mathrm{cm}}^3\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14\times {10}^{3-3}{\mathrm{cm}}^3\\ & \Rightarrow & 14000{\mathrm{mm}}^3=14\times {10}^0{\mathrm{cm}}^3\\ \therefore 14000{\mathrm{mm}}^3& =& 1.4\times {10}^{-1}{\mathrm{cm}}^3\end{array}$

So, the volume $1.4\times {10}^2{\mathrm{cm}}^3$ is not equivalent to $14,000{\mathrm{mm}}^3$.

So, Option (C) is incorrect.

Option (D):

The volume $1.4\times {10}^6{\mathrm{cm}}^3$ is not equivalent to $14,000{\mathrm{mm}}^3$.

Because the correct volume is in ${\mathrm{cm}}^3$ is $1.4\times {10}^{-1}{\mathrm{cm}}^3$.

So, Option (D) is incorrect.

From the obtained vales, it is observed that only (A) is has correct volume, that is $1.4\times {10}^{-5}{\mathrm{m}}^3$.

Therefore, the correct option is (A).