The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are $ 10 \mathrm{~cm} $ and $ 30 \mathrm{~cm} $ respectively. If its height is $ 24 \mathrm{~cm} $.(i) Find the area of the metal sheet used to make the bucket.(ii) Why we should avoid the bucket made by ordinary plastic?

Given:

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are \( 10 \mathrm{~cm} \) and \( 30 \mathrm{~cm} \) respectively.

Its height is \( 24 \mathrm{~cm} \).

To do:

We have to find the area of the metal sheet used to make the bucket.

Solution:

 $\because$ Diameters of the lower and the upper ends are $10\ cm$ and $30\ cm$.

Therefore,

Radius of the lower end $r=\frac{10}{2}$

$=5\ cm$

Radius of the upper end $R=\frac{30}{2}$

$=15\ cm$

Height of the cone $h=24\ cm$

Let $l$ be the slant height of the cone.

We know that,

$l^{2}=h^{2}+( R-r)^{2}$

$\Rightarrow l^{2}=(24)^{2}+( 15-5)^{2}$

$\Rightarrow l^{2}=576+100=676$

$\Rightarrow l=\sqrt{676}=26\ cm$

(i) Required area of the metal sheet$=\pi [r^{2}+( r+R)l]$

$=3.14[5^{2}+( 5+15)26]$

$=3.14[25+520]$

$=3.14\times545$

$=1711.3\ cm^{2}$.

(ii) Plastic is very harmful to the environment, so to keep our environment safe its use should be avoided.

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Updated on: 10-Oct-2022

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