The sum of the length, breath and height of a cuboid box is 20 cm and the total surface area of cuboid is 256 sq. cm. What is the maximum length ( in approximate ) of a stick that can be placed inside the cuboid box ?
Answer & explanation
Correct answer: option 4
We know that,
Diagonal of cuboid = \(\sqrt {l^2 + b^2 + h^2}\)
We have,
Sum of length, breadth and height = 20 cm
l + b + h = 20
= (l + b + h)2 = 400
= l2 + b2 + h2 + 2(lb + bh + hl) = 400
= l2 + b2 + h2 + 256 = 400
= l2 + b2 + h2 = 144
= \(\sqrt {l^2 + b^2 + h^2}\) = 12