question_answer

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? [Use \[\pi =3.14\]]

Answer:

Given, Height of frustum, h = 24 cm.

Diameter of lower end = 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,       \[l=\sqrt{{{h}^{2}}+{{(R-r)}^{2}}}\]

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

\[=\sqrt{576+100}\]

\[=\sqrt{676}\]

\[=26\,cm\]

(i) Area of metal sheet used to make the bucket

= CSA of frustum + Area of base

\[=\pi l(R+r)+\pi {{r}^{2}}\]

\[=\pi [26(15+5)+{{(5)}^{2}}]\]

\[=3.14(26\times 20+25)\]

\[=3.14(520+25)\]

\[=3.14\times 545\]

\[=1711.3\,\,c{{m}^{2}}\]

(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.