If the radii of the circular ends of a bucket of height 40 cm

Height of the bucket = 40 cm

Radius of the upper part of bucket = 35 cm

R1 = 35 cm and

R2 = 14 cm

The volume of the bucket

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

$=\frac{1}{3} \times \frac{22}{7} \times 40\left[(35)^{2}+(14)^{2}+(35 \times 14)\right]$

$=\frac{1}{3} \times \frac{22}{7} \times 40[1225+196+490]$

$=\frac{1}{3} \times \frac{22}{7} \times 40 \times 1911$

$=\frac{1681680}{21}$

$=80080 \mathrm{~cm}^{3}$

Hence, the correct answer is choice (b).