If the inner dimensions of a cuboidal box are 50 cm - 40 cm - 30 cm- then the length of the longest rod that can be placed in the box isA- 50 cmB- 50 -2 cmC- 50 -3 cmD- 120 cm

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Cuboid

If the inner ...

Question

If the inner dimensions of a cuboidal box are 50 cm $\times$ 40 cm $\times$ 30 cm, then the length of the longest rod that can be placed in the box is

50 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

50 \sqrt{2} cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

50 \sqrt{3} cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

120 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $50 \sqrt{2} cm$
Length of the longest rod = length of diagonal

So, the length of the longest rod
$= \sqrt{l^{2} + b^{2} + h^{2}} = \sqrt{(50)^{2} + (40)^{2} + (30)^{2}} = \sqrt{5000} = \sqrt{2500 \times 2} = 50 \sqrt{2} cm$

Suggest Corrections

Similar questions

Assertion: If the inner dimensions of a cuboidal box are $50 c m \times 40 c m \times 30 c m,$ then the length of the longest rod that can be placed in the box is $50 \sqrt{2} c m$ .
Reason: The line joining opposite corners of a cuboid is called its diagonal.
Also, length of longest rod $=$ length of diagonal $= \sqrt{l^{2} + b^{2} + h^{2}}$

Q. The internal dimensions of a rectangular box are

12 c m \times x c m \times 9 c m

. If the length of the longest rod that can be placed in this box is 17 cm; find x.

Q. The internal dimensions of a rectangular box are

12

\times x

\times 9

. If the length of the longest rod that can be placed in this box is

17

cm; find

x

Q. A cubic box of length

120 c m

has to be filled with cuboidal books of dimensions

20 c m \times 12 c m \times 6 c m

. How many such books can be filled in the cubical box?

Q. Find the maximum length of the road that can be kept in a cuboidal box of sides 30cm,24cm,18cm
(Maximum length of the road that can be kept in a cuboidal box is equal to length of the diagonal of the box)

Join BYJU'S Learning Program

If the inner dimensions of a cuboidal box are 50 cm × 40 cm × 30 cm, then the length of the longest rod that can be placed in the box is

The correct option is B 50√2 cmLength of the longest rod = length of diagonal So, the length of the longest rod =√l2+b2+h2=√(50)2+(40)2+(30)2=√5000=√2500×2=50√2 cm

If the inner dimensions of a cuboidal box are 50 cm $\times$ 40 cm $\times$ 30 cm, then the length of the longest rod that can be placed in the box is

The correct option is B $50 \sqrt{2} cm$
Length of the longest rod = length of diagonal

So, the length of the longest rod
$= \sqrt{l^{2} + b^{2} + h^{2}} = \sqrt{(50)^{2} + (40)^{2} + (30)^{2}} = \sqrt{5000} = \sqrt{2500 \times 2} = 50 \sqrt{2} cm$