Work out the length of the longest straight rod that could fit into?

a.

sqrt(6^2 + 6^2 + 6^2) = sqrt(36 + 36 + 36) = sqrt(108) = sqrt(36 * 3) = 6 sqrt(3) cm

or approximately 10.39 cm

b.

sqrt(12^2 + 10^2 + 8^2) = sqrt(144 + 100 + 64) = sqrt(308) = sqrt(4 * 77) = 2 sqrt(77) cm

or approximately 17.55 cm

Answer for Q.no.a,

The cube has each side 6cm

So the length of longest diagonal of the cube is 10.39cm.

Hence, the length of the longest straight rod that would fit in to a cube of side 6cm is 10.39cm.

Answer for Q.no.b,

The length of longest diagonal of the cuboid is 17.55cm.

So the length of the longest straight rod that would fit in to the cuboid is 17.55cm.

a. length = sqrt (3*36)= 6sqrt3 cm =10.39 cm [ diagonal of cube= sidex sqrt3 ]

b. length = sqrt( 144+ 100 + 64)= 17.5499 cm[ diagonal of cuboid= sqrt(a^2+b^2+c^2) ]