Question

The diameters of the lower and upper ends of a bucket in the form of a frustum of 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 ?

Answer 1

Given, Height of frustum, h = 24 cm.
Diameter of lower end, r = 10 cm.
$\therefore$ Radius of lower end, r = 5 cm.
Diameter of upper end = 30 cm.
$\therefore$ Radius of upper end, R= 15 cm,
Slant height, $l=\sqrt{h^2+(R-r{)}^2}$
$=\sqrt{(24{)}^2+(15-5{)}^2}$
$=\sqrt{576+100}$
$=\sqrt{676}$
$=26cm$
(i) Area of metal sheet used to make the bucket
= CSA of frustum + Area of base
= $\pi l(R+r)+\pi r^2$
= $\pi \left[26\right(15+5)+(5{)}^2]$
= $3.14(26\times 20+25)$
= $3.14(520+25)$
= $3.14\times 545$
= $1711.3c{m}^2$
(ii) We should avoid the bucket made by ordinary plastic because plastic is harmful to the environment and to protect the environment its use should be avoided.