Question

Volume of the largest cut diamond is 1.84 cubic inches. What is its volume in cubic centimetre and cubic metres? [1 inch = 2.54 cm]

Answer 1

Hint: $1inch=2.54cm=0.0254m$
Prerequisite: System of Units
Step 1: Given data:
The volume of diamond, $V=1.84inc{h}^3$
Step 2: Calculate the value of $1inc{h}^3$ in terms of $c{m}^3$.
$$\begin{gathered} 1cubicinch={(1inch)}^3 \\ ={(2.54cm)}^3 \\ \Rightarrow 1inc{h}^3=16.387c{m}^3 \end{gathered}$$
Step 3: Convert the volume of the diamond from cubic inches into $c{m}^3$.
$$\begin{gathered} Volumeofdiamond,V=1.84inc{h}^3 \\ =1.84\times 1inc{h}^3 \\ =1.84\times 16.387c{m}^3 \\ \Rightarrow V=30.152c{m}^3(approx.) \end{gathered}$$
Step 4: Calculate the value of $1inc{h}^3$ in terms of $m^3$.
$$\begin{gathered} 1cubicinch={(1inch)}^3 \\ ={(0.0254cm)}^3 \\ \Rightarrow 1inc{h}^3=16.387\times {10}^{-6}{m}^3 \end{gathered}$$

Step 5: Convert the volume of the diamond from cubic inches into $m^3$.
$$\begin{gathered} Volumeofdiamond,V=1.84inc{h}^3 \\ =1.84\times 1inc{h}^3 \\ =1.84\times 16.387\times {10}^{-6}{m}^3 \\ \Rightarrow V=30.152\times {10}^{-6}{m}^3(approx.) \end{gathered}$$
Thus, the volume of diamond in cubic centimeters and cubic metres is $\mathbf{30}\mathbf{.}\mathbf{152}\mathbf{}\mathit{c}{\mathit{m}}^{\mathbf{3}}$ and $\mathbf{30}\mathbf{.}\mathbf{152}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{}{\mathit{m}}^{\mathbf{3}}$ respectively.