Question

plz answer it as soon as possible..​

Answer 1

Answer: The total surface area of the given cuboid is 1900 $cm^{2}$

Step-by-step explanation:

The formula for the diagonal of a cuboid is given by,

$\sqrt{l^2+b^2+h^2}$, where l, b, h are the length ,breadth and height of the cuboid respectively.

$\sqrt{l^2+b^2+h^2}$=15$\sqrt{5}$

on squaring both sides,

$l^2+b^2+h^2=15*15*\sqrt{5} *\sqrt{5}$

$l^2+b^2+h^2=1125$

Also , in the question given,

sum of length,breadth and height =55 cm

l+b+h=55 cm

Now using,algebraic identity,

$(l+b+h)^2= l^2+b^2+h^2+ 2(lb+bh+hl)$

Putting the value of (l+b+h)=55cm and the value of $l^2+b^2+h^2=1125$ in the above equation,

$(55^2)$=1125+2(lb+bh+hl)

3025-1125=2(lb+bh+hl)

1900=2(lb+bh+hl)

Therefore the total surface area of the cuboid is 1900 $cm^{2}$