Question

What is the Maximum Length of a Pencil that can be placed in a Rectangular Box of Dimensions (8cm × 6cm × 5cm)?
(Given √5 = 2.24)

(a) 8 cm
(b) 9.5 cm
(c) 19 cm
(d) 11.2 cm

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Answer 1

(d) 11.2 cm is the answer

Answer 2

Given:-

Dimensions of Rectangular box ( Cuboid ) = ( 8 cm × 6 cm × 5 cm )

Note:- Given √5 = 2.24

To Find:-

Maximum Length of a Pencil that can be placed in a Rectangular Box.

Solution:-

We know that the maximum length of a pencil can be placed in a rectangular box ( Cuboid ) that will be Diagonal of the box.

So, Diagonal of Cuboid ⇒ $\sqrt{L^{2} + B^{2} + H^{2}}$

                                       ⇒ $\sqrt{(8 cm)^{2} + (6 cm)^{2} + (5 cm)^{2}}$

                                       ⇒ $\sqrt{(64 + 36 + 25) cm^{2}}$

                                       ⇒ $\sqrt{125 cm^{2}}$

                                       ⇒ 11.18 cm ≈ 11.2 cm

∴ Maximum Length of a pencil that can be placed in a Rectangular Box is 11.2 cm.

Hence, Option (d) is correct.

Some important terms:-

• Diagonal of Cuboid = $\sqrt{L^{2} + B^{2} + H^{2}}$

• Diagonal of Cube = √3 × side

• Volume of Cuboid = ( Length × Breadth × Height )

• Volume of Cube = ( Side )³