Fig. $1$ shows a rectangular piece of cardboard $ABCD$ of sides $10$ cm and $20$ cm. A trape

Question

Fig. $1$ shows a rectangular piece of cardboard $ABCD$ of sides $10$ cm and $20$ cm. A trapezium shape is cut out from each corner, to give the shape shown in Fig. $2$. This shape consists of $2$ isosceles triangles and $3$ rectangles of different sizes. The remaining cardboard shown in Fig. $2$ is folded along the dotted lines, to form a closed triangular prism shown in Fig. $3$. Show that the volume $V$cm$^{3}$ of the closed triangular prism is given by $V=\frac{1}{5}\left( {{h}^{4}}-10{{h}^{3}}-25{{h}^{2}}+250h \right)$.[4] Use differentiation to find the maximum value of $V$, proving that it is a maximum.[5]

Accepted Answer

(i) $V=\frac15(h^4-10h^3-25h^2+250h)$ (ii) $V_{\max}=\frac{1125}{16}\text{ cm}^3$ at $h=\frac52\text{ cm}$

2015 MJC P2 Q2

2015 MJC P2 Q2

Video Solution:

Solution:

Solution locked