Question

A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1m2 costs ₹20.

Answer 1

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\huge{\underline{\color{purple}{\rm{Question}}}}}$

A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine

(i) The area of the sheet required for making the box.

(ii) The cost of sheet for it, if a sheet measuring 1m2 costs ₹20.

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\huge{\underline{\color{green}{\rm{Answer}}}}}$

(i)${\sf{5.45m^2}}$

(ii)${\sf{Rs109}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{2pt}}} \end{gathered}$

${\large{\sf{(i) The\:area\:of\:the\:sheet\:required\:for\:making\:the\:box.}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{2pt}}} \end{gathered}$

${\large{\underline{\underline{\color{orange}{\rm{To\:Find:}}}}}}$

${\large{\sf{Area\:of\:sheet\:required\:for\:making\:box=?}}}$

${\large{\underline{\underline{\color{purple}{\rm{Given}}}}}}$

${\large{\sf{l=1.5m}}}$

${\large{\sf{b=1.25m}}}$

${\large{\sf{h=65cm=\frac{65}{100}=0.65m}}}$

${\large{\underline{\rm{Here}}}}$

${\large{\sf{l=length}}}$

${\large{\sf{b=breadth}}}$

${\large{\sf{h=height}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\large{\underline{\underline{\sf{Formula\:Using}}}}}$

${\large{\underline{\boxed{\color{red}{\sf{2(lb+bh+hl)}}}}}}$

${\large{\underline{\rm{Here}}}}$

${\large{\sf{l=length}}}$

${\large{\sf{b=breadth}}}$

${\large{\sf{h=height}}}$

$\begin{gathered} \\ {\rule{200pt}{2pt}} \end{gathered}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\qquad{\qquad{\qquad{\quad{\color{blue}{\large{\underline{\sf{Solution}}}}}}}}}$

${\qquad{\qquad{\qquad{\quad{\large{\underline{\boxed{\sf{2(lb+bh+hl)}}}}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{As\:it\:is\:opened\:at\:the\:top\:so\:l\times b\:will\:be\:only\:one\:time}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{\therefore Formula=lb+2(bh+hl)}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{1.5\times 1.25+2(1.25\times 0.65+0.65\times 1.5}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{1.875+2(0.8125+0.975)}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{1.875+2(1.7875)}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{1.875+3.575}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{\longmapsto 5.45}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\large{\color{green}{\sf{Area\:of\:sheet\:required\:for\:making\:box=\boxed{5.45m^2}}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\large{\sf{The\:cost\:of\:sheet\:for\:it,\:if\:a\:sheet\:measuring\:1m^2\:costs\: ₹20.}}}$

${\large{\underline{\underline{\purple{\rm{Given}}}}}}$

${\large{\sf{Given\:Cost\:for\:1m^2=Rs20}}}$

${\large{\underline{\underline{\color{orange}{\rm{To\:Find:}}}}}}$

${\large{\sf{Cost\:of\:sheet=?}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\qquad{\qquad{\qquad{\large{\underline{\underline{\color{blue}{\sf{Solution}}}}}}}}}$

${\qquad{\qquad{\quad{\large{\sf{Area\:of\:sheet=5.45m^2}}}}}}$

${\qquad{\qquad{\quad{\large{\sf{5.45m^2\times 20}}}}}}$

${\qquad{\qquad{\quad{\large{\sf{\longmapsto 109}}}}}}$

${\large{\color{green}{\sf{Cost\:of\:sheet=\boxed{Rs109}}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{9pt}}} \end{gathered}$