Year 11 Maths - Methods Polynomials

Applications Of Polynomial Functions

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Questions

Question 1

28691

A \(10~\text{cm} \times 7~\text{cm}\) rectangular piece of cardboard has equal square corners with side \(x~\text{cm}\) cut out and folded up to make a box. Express the volume of the box \(V\), in terms of \(x\).

Answer

\(V = 4{x^3} - 34{x^2} + 70x\)

Worked Solution

\begin{align}
&\text {Length }=10-2x \\
&\text { Width }=7-2x \\
&\text {Height }=x \\
&\begin{aligned}
V&=x(10-2x)(7-2x) \\
&=x\left(70-20x-14x+4 x^{2}\right) \\
V&=4 x^{3}-34 x^{2}+70 x
\end{aligned}
\end{align}

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