Question

The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is $5\sqrt{5}cm.$ Its surface area is

• A. $361c{m}^2$
• B. $125c{m}^2$
• C. $236c{m}^2$
• D. $486c{m}^2$

Answer 1

The correct option is C

$236c{m}^2$

Let x, y, z be the dimensions of a cuboid, $\text{then x+y+z}=19cm$

$\text{and diagonal}=\sqrt{x^2+y^2+z^2}=5\sqrt{5}$

$\text{Squaring,}{x}^2+y^2+z^2=(5\sqrt{5}{)}^2=125$

$Now,x+y+z=19$

Squaring both sides,

$x^2+y^2+z^2+2(xy+yz+zx)=361$

$125+2(xy+yz+zx)=361$

$\therefore 2(xy+yz+zx)=361-125=236$

$\therefore \text{Surface area}=236c{m}^2$