Q47P - Chemistry: Molecular Nature Of Matter And Change

Question

A cylindrical tube 9.5 cm high and 0.85 cm in diameter is used to collect blood samples. How many cubic decimeters (dm³) of blood can it hold (V of a cylinder = πr²h)?

Step-by-Step Solution

Answer

The volume of blood that can hold by the cylindrical tube is 0.0054 dm³ .

Step 1: Find the radius of the cylindrical tube

The diameter of the cylindrical tube is given as 0.85 cm.

The height of the cylindrical tube is given as 9.5 cm.

The radius of the cylindrical tube can be calculated as follows:

$\mathit{R}\mathit{a}\mathit{d}\mathit{i}\mathit{u}\mathit{s}\mathbf{ }\mathbf{\left(}\mathit{r}\mathbf{\right)}\mathbf{=}\frac{\mathbf{d}\mathbf{i}\mathbf{a}\mathbf{m}\mathbf{e}\mathbf{t}\mathbf{e}\mathbf{r}}{\mathbf{2}}$

Substitute the value of diameter to obtain the radius.

$r=\frac{0.85cm}{2}=0.425cm$

Therefore, the radius of the cylindrical tube is 0.425 cm.

Step 2: Calculate the volume of the cylindrical tube

Use the volume of a cylinder formula.

$\mathit{V}\mathbf{=}\mathit{\pi }{\mathit{r}}^{\mathbf{2}}\mathit{h}$

Here,

V is the volume of a cylinder.

r is the radius of a cylinder.

h is the height of a cylinder.

$\pi$ is the constant which equals 3.14159.

Substitute 3.14159 for $\pi$, 0.425 cm for r and 9.5 cm for h into the above equation.

$\begin{array}{rcl}V& =& 3.14159\times {(0.425cm)}^2\times 9.5cm\\ & =& 5.4c{m}^3\end{array}$

Therefore, the volume of the cylindrical tube is 5.4cm³.

Step 3: Convert cubic centimeters into cubic decimeters

The unit conversion equation for the relationship between cm³ and dm³ is given below:

1dm³ = 1000cm³

The unit conversion factor for converting cm³ into dm³ is given below:

$\frac{1d{m}^3}{1000c{m}^3}$

By using the above conversion factor, the volume of the cylindrical tube can be converted from cubic centimeters to cubic decimeters as shown below:

$\begin{array}{rcl}V& =& 5.4\cancel{c{m}^3}\times \frac{1d{m}^3}{1000 \cancel{c{m}^3}}\\ & =& 0.0054d{m}^3\end{array}$

Hence, the volume of blood that can hold by the cylindrical tube is 0.0054dm³.