Question

The length breadth and height of a room are 12 metre 10 metre and 9 metre respectively find the total surface area of the room

Answer 1

Solution :

Diagram show :

$\setlength{\unitlength}{0.68cm}\begin{picture}(12,4)\linethickness{0.3mm}\put(6,6) {\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{12m}}\put(4,6.3){\sf{10m}}\put(10,7.5){\sf{9m}}\end{picture}$

$\underline{\boldsymbol{According\:to\:the\:question\::}}}$

We know that formula of the total surface area of cuboid :

$\boxed{\bf{2(lb+bh+lh)\:\:\:(sq.unit)}}}}$

We have;

• Length of room = 12 m
• Breadth of room = 10 m
• Height of room = 9 m

$\longrightarrow\tt{Total\:surface\:area\:_{(room)}=2(Length\times breadth + Breadth\times height +length\times height)}\\\\\longrightarrow\tt{Total\:surface\:area\:_{(room)}=2[(12\times 10)+(10\times 9)+(12\times 9)]}\\\\\longrightarrow\tt{Total\:surface\:area\:_{(room)}=2[120+90+108]}\\\\\longrightarrow\tt{Total\:surface\:area\:_{(room)}=2[318]}\\\\\longrightarrow\tt{Total\:surface\:area\:_{(room)}=(2\times 318)m^{2}}\\\\\longrightarrow\bf{Total\:surface\:area\:_{(room)}=636\:m^{2}}$