## Related questions with answers

(a) A rectangular gasoline tank can hold 50.0 kg of gasoline when full. What is the depth of the tank if it is 0.500-m wide by 0.900-m long? (b) Discuss whether this gas tank has a reasonable volume for a passenger car.

Solution

Verified$\textbf{(a)}$ Here the mass of the gasoline

$\begin{align*} m_{\text{G}} = 50.0\,\mathrm{kg} \end{align*}$

Now according to the table 11.1, the density of the rock is

$\begin{align*} \rho_{\text{G}} = 0.68\times 10^{3}\,\mathrm{kg\,m^{-3}} \end{align*}$

The width of the gasoline tank

$\begin{align*} w_{\text{T}} = 0.500\,\mathrm{m} \end{align*}$

The length of the gasoline tank

$\begin{align*} l_{\text{T}} = 0.900\,\mathrm{m} \end{align*}$

Now as we know the volume of a rectangle tank having width $w_{\text{T}}$, length $l_{\text{T}}$, and height $h_{\text{T}}$ is

$\begin{align*} V_{\text{G}} = V_{\text{T}} = w_{\text{T}} \times l_{\text{T}} \times h_{\text{T}}\tag{1} \end{align*}$

Now as we know the density is the mass per unit volume of a substance or object. In equation form, density is defined as

$\begin{align*} \rho_{\text{G}} = \frac{m_{\text{G}}}{V_{\text{G}}}\tag{2} \end{align*}$

Where $m$ is the mass and $V$ is the volume of the substance or the object. Now to calculate the height or depth of the tank, we use the above equations (1) and (2) and we get

$\begin{align*} \rho_{\text{G}} & = \frac{m_{\text{G}}}{w_{\text{T}} \times l_{\text{T}} \times h_{\text{T}}}\tag{3} \end{align*}$

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