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Ex.11.3 Q10 Mensuration Solution - NCERT Maths Class 8

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Question

A company packages its milk powder in cylindrical container whose base has a diameter of \(14\,\rm{ cm}\) and height \(20\,\rm{ cm.}\) Company places a label around the surface of the container (as shown in the figure). If the label is placed \(2 \,\rm{cm}\) from top and bottom, what is the area of the label.

 Video Solution
Mensuration
Ex 11.3 | Question 10

Text Solution

What is Known?

Label placed on container is in the form of a cylinder.

What is unknown?

Area of the label placed on container.

Reasoning:

The length of rectangular sheet will be equal to the circumference of the circle.

Visually, area of the label on the cylinder will be equal to lateral surface area of the cylinder.

Steps:

Height of the label\((h)\) \( = 20\,\rm{cm} \,– \,2 \times 2\, \rm{cm} =16\, \rm{cm}\)

Radius of the label

\[\begin{align} = \frac{{14}}{2}\,{\rm{cm}} = 7\,{\rm{cm}} \end{align}\]

Label in the form of a cylinder having its Radius and height as \(7\,\rm{cm}\) and \(16\,\rm{cm.}\)

Area of the label \(=\) Lateral surface area of the cylinder

\[\begin{align}&=2\pi rh \\&= 2 \times \frac{{22}}{7} \times 7\,{\rm{cm}} \times 16\,{\rm{cm}}\\ &= 704\,{\rm{c\rm{m}}^2}\end{align}\]

Thus, the required area of the label is \(704\,{\rm{cm}^2}.\)

  
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