The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm.
Question:

The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.

Solution:

Height of the bucket = 30 cm.

$r_{1}=21 \mathrm{~cm}$

$r_{2}=7 \mathrm{~cm}$

Therefore,

Capacity of the bucket

$=\frac{\pi h}{3}\left[r_{1}^{2}+r_{1} r_{2}+r_{2}^{2}\right]$

$=\frac{22}{7} \times \frac{30}{3}\left[(21)^{2}+21 \times 7+(7)^{2}\right]$

$=20020 \mathrm{~cm}^{3}$

$=20.02$ litres

The slant height of the bucket

$l=\sqrt{h^{2}+\left(r_{1}-r_{2}\right)^{2}}$

$=\sqrt{900+(21-7)^{2}}$

$=\sqrt{900+196}$

$=\sqrt{1096}=33.105 \mathrm{~cm}$

$=\sqrt{900+(21-7)^{2}}$

$=\sqrt{900+196}$

$=\sqrt{1096}=33.105 \mathrm{~cm}$

$=\pi\left(r_{1}+r_{2}\right) \times l$

$=\pi(21+7) \times 33.1$

$=88 \times 33.1$

$\approx 2913 \mathrm{~cm}^{2}$

Area of the base

$=\pi r^{2}$

$=\frac{22}{7} \times 7^{2}$

$=154$

Total sheet required to make this bucket

$=2913+154$

$=3067 \mathrm{~cm}^{2}$