Question

Volume of Fruit Crate $A$ fruit crate has square ends and is twice as long as it is wide.
$\left(a\right)$ Find the volume of the crate if its width is $20in$.
$\left(b\right)$ Find a formula for the volume $V$ of the crate in terms of its width $x$.

Answer 1

Given:

The volume of Fruit Crate $A$ fruit crate has square ends and is twice as long as it is wide.

To find:

(i) The volume of the crate when its width is $20in$.

Explanation:

The width of the fruit crate $A$ has $20in$, also given that the length is twice as it is wide and is one of the sides of a square end.

$width=20in$

$\begin{array}{rcl}length& =& 2\times w\\ & =& 2\times 20\\ & =& 40in\end{array}$

$height=20in$

We know that, $Volume=width\times length\times height$.

Substitute $width$ as $20$, $length$ as $40$ and $height$ as $20$ in the above formula.

$\begin{array}{rcl}Volume& =& 20\times 40\times 20\\ & =& 16000cubicinches\end{array}$

Therefore, the volume of the fruit crate is $16000cubicinches$.

To find:

(ii) Find a formula for the volume $V$ of the crate in terms of its width $x$.

Explanation:

Let width of the fruit crate $A$ be $x$, also given that the length is twice as it is wide and is one of the sides of a square end.

$width=x$

$\begin{array}{rcl}length& =& 2\times w\\ & =& 2\times x\\ & =& 2x\end{array}$

$height=x$

We know that, $Volume=width\times length\times height$.

Substitute $width$ as $x$, $length$ as $2x$ and $height$ as $x$ in the above formula.

$\begin{array}{rcl}Volume& =& x\times 2x\times x\\ & =& 2x^3\end{array}$

Therefore, the general volume of the fruit crate is $2x^3$.