Question

The sum of length,breadth and depth of a cuboid is 19 cm and length of diagnol is 11 cm .Find the surface area of cuboid??

Answer 1

HERE,

$l + b + h = 19cm$

$length \: of \: diagonal = 11cm$

$we \: know \: that$

$diagonal = \sqrt{ {l}^{2} + {b}^{2} + {h}^{2} }$

$11 = \sqrt{ {l}^{2} + {b}^{2} + {h}^{2} }$

by squaring both sides

$121 = {l}^{2} +{ b }^{2} + {h}^{2} ..........(1)$

NOW,
WE HAVE,

$l + b + h = 19$
squaring both sides we get

${(l + b + h)}^{2} = {19}^{2}$

we know that,
(a+b+c)^2

$= {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc \\ + 2ac$
using this formula

we get,

$l^{2}+b^{2}+h^{2}+2lb+2bh \\ + 2lh = 361$

$121 + 2(lb + bh + lh) = 361 \\ ....................(from \: 1)$


$2(lb + bh + lh) = 361 - 121$

$2(lb + bh + lh) = 240.......(2)$

we know that,
total surface area of cuboid
=2(lb+bh+lh)..............................(3)


from (2) & (3)

$surface \:area = 240 {cm}^{2}$

Therefore,
the surface area of cuboid is 240 sq. cm

$hope \: this \: helps \: you$