Question

The cylinder is placed in a box that is a cube of side 14 cm. Calculate the percentage of the volume of the box that is occupied by the cylinder

Answer 1

Hey Aabid !

Answer:

78.57 %

Step-by-step explanation:

Given :

A cylinder placed in a cubical box.

Side of cubical box = 14 cm

To find :

The percentage of the volume of the box that is occupied by the cylinder.

Concept :

Assuming that the placed cylinder fits perfectly and to the maximum extent it could fit to,

The percentage of the volume of the box that is occupied by the cylinder = $\frac{Volume \ of \ the \ Cylinder}{Volume \ of \ the \ Cubical \ box} \times 100\%$

Formulae :

Volume of a Right Circular Cylinder = πr²h

• Where r is the radius of the base of the cylinder.
• Where h is the height of the cylinder.

Volume of a Cube = s³

• Where s is the side of the cube.

Procedure :

Height of the cylinder = 14 cm

Radius of the base of the Cylinder  = 7 cm

[∵ 2r = 14 cm, ∴ r = 7 cm]

Refer the attached picture for how the above values have come. In the picture, the cylinder's base might look elliptical, but it is a circle if you look from the top view [Attached too :)]

Hence the volume of the cylinder assuming that π = 22/7,

V = πr²h units³

⇒ V = (22/7)(7)(7)(14) cm³

⇒ V = 22 × 7 × 14 cm³

⇒ V = 2156 cm³

∴ Volume of the Cylinder = 2156 cm³.

Volume of the Cubical box = s³ units³

⇒ V = (14)³ cm³

⇒ V = 2744 cm³

∴ Volume of the Cubical box = 2744 cm³.

Hence, The percentage of the volume of the box that is occupied by the cylinder = $\frac{2156}{2744} \times 100 \%$

⇒ $\frac{11}{14} \times 100 \%$

⇒ $\frac{550}{7} \%$

⇒ 78.57 % [Approx]

Thanks !