The diameters of the lower and upper ends of a bucket in the form of a frustum f a cone are $10\ cm$ and $30\ cm$ respectively. If its height is $24\ cm$, find:

$( i)$ The area of the metal sheet used to make the bucket.
$( ii)$ Why we should avoid the bucket made by ordinary plastic? [Use $\pi=3.14$ ]

$( i)$ The area of the metal sheet used to make the bucket.

$( ii)$ Why we should avoid the bucket made by ordinary plastic? [Use $\pi=3.14$ ]

Solution:

$\therefore$ 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 $l$ is the slant height of the cone,

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

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

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

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

$( i)$ 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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