Question

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are $10cm$ and $30cm$ respectively. If its height is $24cm$, 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 $\pi =3.14$)

Answer 1

Given: Height of the frustrum $\left(h\right)=24$ cm

radius of lower end of bucket $\left(r_1\right)=\frac{10}{2}=5cm$

Radius of upper end of bucket $\left(r_2\right)=\frac{30}{2}=15cm$

$\therefore$ Slant height $\left(l\right)=\sqrt{h^2+(r_2-r_1{)}^2}$

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

$=\sqrt{(24{)}^2+(10{)}^2}$

$=\sqrt{576+100}=\sqrt{676}=26cm$

Now, Area of the metal sheet used to make the bucket = T.S.A of the

bucket (excluding the upper end)

Total Surface Area(TSA) $=\pi (r_1+r_2)l+\pi r_1^2$

$=\left(3.14\right)(15+5)\left(26\right)+3.14(5{)}^2$

$=1632.8+78.5=1711.3c{m}^2$

(b) We should avoid the bucket made by ordinary plastic as plastic is non biodegradable and hazardous to environment.